How to solve two-step equations - Math

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Question

Solve the equation for .

$\frac{4}{x}+3=9$

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Answer

$\small \small \frac{4}{x}+3=9$

Subtract from both sides and simplify.

$\small \small \frac{4}{x}+3-3=9-3=6$

$\small \small \frac{4}{x}=6$

Multiply both sides by to remove it from the denominator.

$\small \small \frac{4}{x}(x)=6(x)$

$\small 4=6x$

Divide both sides by .

$\small \frac{4}{6}=\frac{6x}{6}$

Simplify the fraction.

$\small x=\frac{4}{6}=\frac{2}{3}$

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Question

Solve for $\small a$ .

$\frac{12}{a}-7=-1$

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Answer

$\frac{12}{a}-7=-1$

Add 7 to both sides.

$\frac{12}{a}-7+7=-1+7$

$\frac{12}{a}=6$

Multiply both sides by $\small a$ .

$\frac{12}{a}(a)=6a$

Divide both sides by 6.

$\frac{12}{6}=\frac{6a}{6}$

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Question

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Answer

This is a two-step equation. First you must add the decimals up to have a singular variable element

$\left ( 2.4+1.6\right )X=16$

Then divide both sides by 4:

$\frac{4X}{4}=\frac{16}{4}$

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Question

Solve for

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Answer

The goal is to get alone on one side. Therefore you subtract from both sides to get . Then divide both sides by to get alone.

.

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Question

Solve the equation for . (Round to two decimal places).

$\small 1.22n+4=3.5$

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Answer

$\small 1.22n+4=3.5$

Subtract from both sides of the equation, and simplify.

$\small 1.22n+4-4=3.5-4$

$\small \small 1.22n=-0.50$

Divide both sides by . Be careful of the negative sign.

$\small \frac{1.22n}{1.22}=-\frac{0.50}{1.22}$

$\small n=-0.41$

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Question

Josie buys $\$12.38$ worth of groceries. The sales tax is . If she pays with $\$20$ , how much change should she get?

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Answer

The sales tax is $12.38\cdot 0.03875=0.479$

The total grocery bill is .

The change is .

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Question

$15=\frac{Y}{3}-9$

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Answer

First add 9 to both sides:

$15+(9)=\frac{Y}{3}-9+(9)$

$24=\frac{Y}{3}$

Then multiply both sides by 3:

$24\left ( 3\right )=\frac{Y}{3}\left ( 3\right )$

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Question

Solve for .

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Answer

To solve, we must perform the same operations to both sides of the equation.

Add 7 to both sides.

Divide both sides by 3.

$\frac{3n}{3}=\frac{19}{3}$

$n=\frac{19}{3}$

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Question

Solve for :

$\frac{12}{x} + 9 = 13$

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Answer

This equation can be solved in three steps.

First, subtract from both sides of the equation to isolate the variable and its coefficient on the left side of the equation.

$\frac{12}{x} + 9 = 13$

$\rightarrow (\frac{12}{x} + 9) - 9 = (13) - 9$

$\rightarrow \frac{12}{x} = 4$

Now multiply both sides by since cannot be solved for while it is in the denominator.

$(\frac{12}{x}) \times x = (4) \times x$

$\rightarrow 12 = 4x$

Finally, divide both sides by to isolate and find the solution.

$\frac{(12)}{4} = \frac{(4x)}{4}$

$\rightarrow 3 = x$

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Question

Solve for $\small x$ .

$(2x\div4) +5 = 25$

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Answer

$(2x\div4) +5 = 25$

We need to isolate $\small x$ . First, subtract $\small 5$ from both sides.

$(2x\div4) +5-5 = 25-5$

$(2x\div4) = 20$

Multiply both sides by $\small 4$ .

$2x\div4 4= 204$

Finally, divide both sides by $\small 2$ .

$\frac{2x}{2}=\frac{80}{2}$

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Question

Solve for the value of $\small a$ .

$\frac{a}{4}+3=12$

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Answer

$\frac{a}{4}+3=12$

We need to work to isolate the variable using inverse functions.

Subtract $\small 3$ from both sides.
$\frac{a}{4}+3-3=12-3$

$\frac{a}{4}=9$

Multiply both sides by $\small 4$ .

$(4)\frac{a}{4}=(4)(9)$

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Question

$x=\frac{2}{3}*18$

Solve for .

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Answer

$x=\frac{2}{3}18$

From here, you can either plug this into your calculator, or take the equation in pieces:

$x=\frac{218}{3}$

$x=\frac{36}{3}$

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Question

$\frac{2}{3}*(x+5)=12$

Solve for .

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Answer

To solve $\frac{2}{3}(x+5)=12$ , first we need to get rid of the fraction. Dividing by a fraction is the same as multiplying by a reciprocal, so multiply both sides by $\frac{3}{2}$ .

$\frac{2}{3}(x+5)=12$

$\frac{3}{2}\frac{2}{3}(x+5)=12\frac{3}{2}$

$x+5=12\frac{3}{2}$

$x+5=\frac{12*3}{2}$

$x+5=\frac{36}{2}$

Subtract from both sides.

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Question

A glass jar is filled to the top with 100 blue marbles, 75 red marbles, and 25 yellow marbles. Each time a marbles is picked from the jar, it must be returned to the jar before another marble is picked again. What is the probability of picking a red marble?

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Answer

First, find the total number of marbles in the glass jar: marbles in total.

It is given that there are 75 red marbles, thus: .

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Question

$\frac{2}{3}x=10$

Solve for .

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Answer

To solve $\frac{2}{3}x=10$ , we need to get rid of the fraction. To do that, we multiply both sides by the reciprocal of that fraction.

$\frac{3}{2}\frac{2}{3}x=10\frac{3}{2}$

$x=10\frac{3}{2}$

From here, you can either plug that fraction into your calculator or solve in pieces.

$x=\frac{103}{2}$

$x=\frac{30}{2}$

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Question

$\frac{3}{4}x=118+2$

Solve for .

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Answer

To solve for , we need to isolate our variable. That means that we want ONLY the on the left side of the equation.

First, combine our like terms on the right side.

$\frac{3}{4}x=118+2$

$\frac{3}{4}x=120$

Now divide both sides by $\frac{3}{4}$ . Remember, dividing by a fraction is the same as multiplying by the reciprocal, so we're going to multiply both sides by $\frac{4}{3}$ .

$\frac{3}{4}x\frac{4}{3}=120\frac{4}{3}$

Since $\frac{3}{4}\frac{4}{3}=\frac{12}{12}=1$ , we can ignore it.

$x=\frac{120}{1}\frac{4}{3}$

$x=\frac{480}{3}$

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Question

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Answer

This is a two-step equation. First simplify the whole numbers by adding 6 to both sides:

$24+\left ( 6\right )=2X-6+\left ( 6\right )$

Then divide both sides by 2

$\frac{30}{2}=\frac{2X}{2}$

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Question

Solve for :

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Answer

We have two steps to this problem. Remember our end result is to get isolated on one side of the equation.

First we add to each side, cancelling out the on the left side. This brings the equation to .

Remember to get rid of a number we perform the opposite operation. The is multiplied with the , therefore to cancel it out we will divide by .

divided by equals . What we do to one side we must do to the other, therefore we divide by also. This becomes .

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Question

Simplify:

$(2x^{2}+5) (3x^{3}+ 3)$

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Answer

The requires the FOIL method (first, outside, inside, last).

Multiplying the first two monomials $2x^2 \cdot 3x^3$ equals $6x^{5}$ .

The outside two are $2x^{2} \cdot 3$ which equals $6x^{2}$ .

The two inside monomials are $5 \cdot 3x^3$ which equals .

The last two are $5\cdot 3$ which is .

All together this becomes $6x^{5}+15x^{3}+6x^{2}+15$ .

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Question

What is if ?

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Answer

Plugging in for gives .

=

= .

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