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

Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.

6.EE.7

Solve real-world and mathematical problems by writing and solving equations of the form x + p = q; x - p = q; px = q; and x/p = q for cases in which p, q, and x are all nonnegative rational numbers.

6.EE.B

No additional information available.

6.NS.3

Fluently add, subtract, multiply, and divide multi-digit decimals using a standard algorithm for each operation.