GMAT Math : Solving linear equations with one unknown

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Example Question #21 : Solving Linear Equations With One Unknown

Solve for : $\frac{3}{2}x+\frac{1}{3}=\frac{5}{9}$ .

Possible Answers:

$x=-\frac{4}{27}$

$x=-\frac{27}{4}$

$x=\frac{27}{4}$

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

$x=\frac{4}{27}$

Correct answer:

$x=\frac{4}{27}$

Explanation:

To solve for , we need to isolate on one side of the equation:

$\frac{3}{2}x+\frac{1}{3}=\frac{5}{9}$

$\frac{3}{2}x=\frac{5}{9}-\frac{1}{3}$

$\frac{3}{2}x=\frac{5}{9}-\frac{3}{9}$

$\frac{3}{2}x=\frac{2}{9}$

$x=\frac{2}{9}\times\frac{2}{3}$

$x=\frac{4}{27}$

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Example Question #22 : Linear Equations, One Unknown

Solve the following equation:

8x+3-15x=-4-11x+43

Possible Answers:

x=9

x=5

x=-2

x=-9

x=2

Correct answer:

x=9

Explanation:

We start by grouping all of our like terms, so the terms with x are grouped on the left side and the constants are grouped on the right side:

8x+3-15x=-4-11x+43

-7x+3=39-11x

4x=36

x=9

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Example Question #21 : Linear Equations, One Unknown

Solve for : 9x-7=29

Possible Answers:

Correct answer:

Explanation:

In order to solve for in 9x-7=29 , isolate on one side of the equation:

9x-7=29

9x=36

x=4

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Example Question #24 : Linear Equations, One Unknown

Solve for : 3z-9=5z-11

Possible Answers:

$\frac{1}{2}$

Correct answer:

Explanation:

In order to solve for , we need to isolate on one side of the equation:

3z-9=5z-11

-9=2z-11

2=2z

1=z

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Example Question #25 : Linear Equations, One Unknown

Solve for : $\frac{1}{2}y-9=\frac{3}{4}y+6$

Possible Answers:

Correct answer:

Explanation:

In order to solve for , isolate on one side of the equation and simplify:

$\frac{1}{2}y-9=\frac{3}{4}y+6$

$-9=\frac{1}{4}y+6$

$-15=\frac{1}{4}y$

-60=y

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Example Question #26 : Linear Equations, One Unknown

Given $\small f(x)=4x+b$ and $\small f(4)=26$ , find the height of the line's -intercept.

Possible Answers:

Correct answer:

Explanation:

The trick here is recognizing what you are given. In y=mx+b form, is equal to the -intercept. All we need to do is find . Find this by recognizing that f(4)=26 means that the point (4,26) is on this line. More simply, if we plug in 4 for and 26 for (or in other words, f(x) ), we can find .

So this:

$\small f(x)=4x+b$

becomes:

26=4*4+b

26=16+b

$\small b=26-16=10$

So, b=10 .

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Example Question #27 : Linear Equations, One Unknown

Solve for : 7y-21=28

Possible Answers:

Correct answer:

Explanation:

In order to solve for , isolate on one side of the equation and simplify.

First, add 21 to both sides in order to get all constants on one side.

7y-21=28

Then divide by 7 to solve for y.

7y=49

y=7

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Example Question #28 : Linear Equations, One Unknown

Solve for :

$\frac{2}{3}z+9=12$

Possible Answers:

$-\frac{9}{2}$

$-\frac{2}{9}$

$\frac{9}{2}$

$\frac{2}{9}$

Correct answer:

$\frac{9}{2}$

Explanation:

In order to solve the equation, isolate on one side of the equation.

To do this, first subtract 9 from both sides.

$\frac{2}{3}z+9=12$

$\frac{2}{3}z=3$

Then multiply both sides by 3 to move the three to the left hand side.

2z=9

Lastly, divide by 2 on both sides to solve for z.

$z=\frac{9}{2}$

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Example Question #29 : Linear Equations, One Unknown

Solve for :

-4a+8=4

Possible Answers:

$\frac{1}{2}$

$\frac{1}{4}$

$-\frac{1}{2}$

Correct answer:

Explanation:

To solve for a we need to isolate a on one side of the equation and all other numbers on the other side of the equation.

Inorder to do this we first subtract 8 from both sides.

-4a+8=4

Now, we divide by -4 to finish isolating a.

-4a=-4

a=1

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Example Question #30 : Linear Equations, One Unknown

Solve for .

-2(x+5)-7(8-x)=14-(2+x)

Possible Answers:

x=-4.25

x=-13

x=13

x=11.14

Correct answer:

x=13

Explanation:

-2(x+5)-7(8-x)=14-(2+x)

-2x-10-56+7x=14-2-x

-10-56+6x=12

6x=78

x=13

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GMAT Math : Solving linear equations with one unknown

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #21 : Solving Linear Equations With One Unknown

Example Question #22 : Linear Equations, One Unknown

Example Question #21 : Linear Equations, One Unknown

Example Question #24 : Linear Equations, One Unknown

Example Question #25 : Linear Equations, One Unknown

Example Question #26 : Linear Equations, One Unknown

Example Question #27 : Linear Equations, One Unknown

Example Question #28 : Linear Equations, One Unknown

Example Question #29 : Linear Equations, One Unknown

Example Question #30 : Linear Equations, One Unknown

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