High School Math : How to solve two-step equations with decimals in pre-algebra

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #1 : How To Solve Two Step Equations With Decimals In Pre Algebra

\displaystyle 2.4X+1.6X=16

\displaystyle X=?

 

Possible Answers:

\displaystyle 26

\displaystyle 4

\displaystyle 8

\displaystyle 12

\displaystyle 16

Correct answer:

\displaystyle 4

Explanation:

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

\displaystyle 2.4X+1.6X=16

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

\displaystyle 4X=16

Then divide both sides by 4:

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

\displaystyle X=4

Example Question #1 : How To Solve Two Step Equations With Decimals In Pre Algebra

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

\displaystyle \small 1.22n+4=3.5

Possible Answers:

\displaystyle \small n=-6.15

\displaystyle \small n=-0.41

\displaystyle \small n=0.41

\displaystyle \small n=6.15

Correct answer:

\displaystyle \small n=-0.41

Explanation:

\displaystyle \small 1.22n+4=3.5

Subtract \displaystyle 4 from both sides of the equation, and simplify.

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

\displaystyle \small \small 1.22n=-0.50

Divide both sides by \displaystyle 1.22. Be careful of the negative sign.

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

\displaystyle \small n=-0.41

Example Question #505 : High School Math

\displaystyle 2.5x+10=30

Solve for \displaystyle x

Possible Answers:

\displaystyle x=8

\displaystyle x=5

\displaystyle x=2.4

\displaystyle x=10

\displaystyle x=16

Correct answer:

\displaystyle x=8

Explanation:

The goal is to get \displaystyle x alone on one side. Therefore you subtract \displaystyle 10 from both sides to get \displaystyle 2.5x=20. Then divide both sides by \displaystyle 2.5 to get \displaystyle x alone.

\displaystyle 20/2.5=8.

Example Question #4 : How To Solve Two Step Equations With Decimals In Pre Algebra

Josie buys \displaystyle \$12.38 worth of groceries.  The sales tax is \displaystyle 3.875\%.  If she pays with \displaystyle \$20, how much change should she get?

Possible Answers:

\displaystyle \$7.62

\displaystyle \$6.19

\displaystyle \$7.14

\displaystyle \$6.58

\displaystyle \$5.97

Correct answer:

\displaystyle \$7.14

Explanation:

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

The total grocery bill is \displaystyle 12.38+0.48=12.86.

The change is \displaystyle 20-12.86=7.14.

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