Lesson 4: Practice Solving Equations

Practice Solving Equations

Student Summary

When we solve an equation with a variable, we find the value for the variable that makes the equation true. One way to solve the equation is to do the same thing to each side until the variable is alone on one side of the equal sign, and see what is on the other side.

Solve the equation $x+\frac{3}{4}=\frac{7}{8}$ .

The fraction

\frac{3}{4}

is added to the variable

x

$\displaystyle x+\frac{3}{4}=\frac{7}{8}$

So, we can subtract

\frac{3}{4}

from each side of the equation.

$\displaystyle x+\frac{3}{4}-\frac{3}{4}=\frac{7}{8}-\frac{3}{4}$

The variable is alone on one side of the equal sign, and

\frac{1}{8}

is on the other side.

$\displaystyle x=\frac{1}{8}$

When we substitute

\frac{1}{8}

for

x

in the original equation, the equation is true. So, we know

\frac{1}{8}

is the solution.

$\begin{aligned}\displaystyle \frac{1}{8} +\frac{3}{4} &= \frac{7}{8} \\ \displaystyle \frac{7}{8} &= \frac{7}{8}\end{aligned}$

Solve the equation

3.5x=31.5

The variable

x

is multiplied by 3.5.

$\displaystyle 3.5x=31.5$

So, we can divide each side of the equation by 3.5.

$\displaystyle 3.5x \div 3.5=31.5 \div 3.5$

The variable is alone on one side of the equal sign, and 9 is on the other side.

$\displaystyle x = 9$

When we substitute 9 for

x

in the original equation, the equation is true. So, we know 9 is the solution.

$\begin{aligned}\displaystyle 3.5(9)&=31.5 \\ \displaystyle 31.5 &= 31.5\end{aligned}$

Visual / Anchor Chart

Standards

Addressing

6.EE.5

6.EE.7

6.EE.B

6.EE.B.5

6.EE.B.7

6.NS.3

6.NS.B.3