Algebra 1 : How to solve two-step equations

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #1 : How To Solve Two Step Equations

Evaluate the expression (3x + 4y)3 when x = 4 and y = 2.

Possible Answers:

343

64

8000

2744

800

Correct answer:

8000

Explanation:

Plug in 4 for x and 2 for y, giving you (3(4) + 4(2))3, which equals (20)3, equalling 8000.

(3x + 4y)3

(3(4) + 4(2))3

(12 + 8)3

(20)3 = 8000

Example Question #1 : How To Solve Two Step Equations

Evaluate \(\displaystyle (x+3)^2-\frac{18}{2}\) when x = 3.

Possible Answers:

3

9

0

27

–3

Correct answer:

27

Explanation:

First plug 3 in for x, giving you \(\displaystyle (6)^2-\frac{18}{2}\). You square 6, giving you 36, then subtract (18/2), giving you 27.

\(\displaystyle (x+3)^2-\frac{18}{2}\)

\(\displaystyle (3+3)^2-\frac{18}{2}\)

\(\displaystyle (6)^2-9\)

\(\displaystyle 36-9=27\)

Example Question #2 : How To Solve Two Step Equations

Solve for \(\displaystyle x\).

\(\displaystyle 2x - 5 = -3x - 10\)

Possible Answers:

\(\displaystyle x=0\)

\(\displaystyle x=1\)

\(\displaystyle x=-1\)

\(\displaystyle x=3\)

\(\displaystyle x=-3\)

Correct answer:

\(\displaystyle x=-1\)

Explanation:

\(\displaystyle 2x - 5 = -3x -10\)

Add 5 to each side of the equation.

\(\displaystyle 2x = -3x -5\)

Add 3x to each side of the equation.

\(\displaystyle 5x = -5\)

Divide each side of the equation by 5.

\(\displaystyle x = -1\)

Example Question #4 : How To Solve Two Step Equations

Solve for \(\displaystyle n\).

\(\displaystyle 3n+9=0\)

Possible Answers:

\(\displaystyle -6\)

\(\displaystyle \frac{1}{3}\)

\(\displaystyle 3\)

\(\displaystyle -\frac{1}{3}\)

\(\displaystyle -3\)

Correct answer:

\(\displaystyle -3\)

Explanation:

\(\displaystyle 3n+9=0\)

Subtract 9 from both sides of the equation.

\(\displaystyle 3n=-9\)

Divide each side of the equation by 3.

\(\displaystyle n=\frac{-9}{3}\)

\(\displaystyle n=-3\)

Example Question #5 : How To Solve Two Step Equations

Solve for \(\displaystyle x\).

\(\displaystyle -11 - \frac{6}{x} = 13\)

Possible Answers:

\(\displaystyle -4\)

\(\displaystyle -\frac{1}{4}\)

\(\displaystyle \frac{1}{4}\)

\(\displaystyle 4\)

\(\displaystyle 0\)

Correct answer:

\(\displaystyle -\frac{1}{4}\)

Explanation:

\(\displaystyle -11 - \frac{6}{x} = 13\)

Add 11 to each side of the equation.

\(\displaystyle -\frac{6}{x}=24\)

Multiply each side of the equation by \(\displaystyle x\).

\(\displaystyle -6 = 24x\)

Divide each side of the equation by 24.

\(\displaystyle \frac{-6}{24} = x\)

Simplify

\(\displaystyle -\frac{1}{4}\)

Example Question #1 : How To Solve Two Step Equations

Solve for \(\displaystyle x\):

\(\displaystyle \small 7x+3=17\)

Possible Answers:

\(\displaystyle \small x=3\)

\(\displaystyle \small x=4\)

\(\displaystyle \small x=2\)

\(\displaystyle \small x=1\)

Correct answer:

\(\displaystyle \small x=2\)

Explanation:

First, substract 3 from both sides:

\(\displaystyle \small 7x+3-3=17-3\)

\(\displaystyle \small 7x=14\)

Next, divide each side by 7:

\(\displaystyle \small \frac{7x}{7}= \frac{14}{7}\)

\(\displaystyle \small x=2\)

Example Question #2 : How To Solve Two Step Equations

Solve for x:

\(\displaystyle 5x-32=17\)

Possible Answers:

\(\displaystyle 9\frac{4}{5}\)

\(\displaystyle 0\)

\(\displaystyle 1\frac{4}{49}\)

\(\displaystyle 9\frac{4}{19}\)

None of the available answers

Correct answer:

\(\displaystyle 9\frac{4}{5}\)

Explanation:

\(\displaystyle 5x-32=17\)

\(\displaystyle 5x-32+32=17+32\)

\(\displaystyle 5x=49\)

\(\displaystyle x=\frac{49}{5}=9\frac{4}{5}\)

Example Question #6 : How To Solve Two Step Equations

Solve for \(\displaystyle x\):

\(\displaystyle \frac{4}{5}x-12=\frac{4}{3}x+13\)

Possible Answers:

\(\displaystyle -46\frac{7}{8}\)

\(\displaystyle -46\frac{7}{15}\)

None of the available answers

\(\displaystyle 46\frac{7}{8}\)

\(\displaystyle -42\frac{15}{8}\)

Correct answer:

\(\displaystyle -46\frac{7}{8}\)

Explanation:

\(\displaystyle \frac{4}{5}x-12=\frac{4}{3}x+13\)

\(\displaystyle \frac{4}{5}x-\frac{4}{3}x=25\)

\(\displaystyle \frac{12}{15}x-\frac{20}{15}x=25\)

\(\displaystyle -\frac{8}{15}x=25\)

\(\displaystyle x=\frac{-15}{8}\cdot\frac{25}{1}=\frac{-375}{8}=-46\frac{7}{8}\)

Example Question #3 : How To Solve Two Step Equations

Solve for \(\displaystyle m\)

\(\displaystyle 4m+4=8\)

Possible Answers:

\(\displaystyle 8\)

\(\displaystyle 4\)

\(\displaystyle 1\)

\(\displaystyle 2\)

\(\displaystyle 3\)

Correct answer:

\(\displaystyle 1\)

Explanation:

First subtract 4 from both sides.  This gives \(\displaystyle 4m = 4\).  Then divide both sides by 4 to get \(\displaystyle m=1\)

Example Question #10 : How To Solve Two Step Equations

Solve for \(\displaystyle x\):

\(\displaystyle ax-b=c\)

Possible Answers:

\(\displaystyle x=\frac{c+b}{a}\)

None of the other answers

\(\displaystyle x=\frac{a}{c+b}\)

\(\displaystyle x=\frac{c-b}{a}\)

\(\displaystyle x=a(c+b)\)

Correct answer:

\(\displaystyle x=\frac{c+b}{a}\)

Explanation:

To solve for \(\displaystyle x\), add \(\displaystyle b\) to both sides to get \(\displaystyle ax=c+b\). Then, divide both sides by \(\displaystyle a\) to get \(\displaystyle x=\frac{c+b}{a}\).

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