8.3 Solve equations with variables and constants on both sides  (Page 3/5)

Solution

This equation has $2a$ on the left and $5a$ on the right. Since $5>2,$ make the right side the variable side and the left side the constant side.

Subtract $2a$ from both sides to remove the variable term from the left.
Combine like terms.
Subtract 8 from both sides to remove the constant from the right.
Simplify.
Divide both sides by 3 to make 1 the coefficient of $a$ .
Simplify.
Check: Let $a=\mathrm{-5}$ .

Note that we could have made the left side the variable side instead of the right side, but it would have led to a negative coefficient on the variable term. While we could work with the negative, there is less chance of error when working with positives. The strategy outlined above helps avoid the negatives!

Solution

Since $\frac{3}{2}>\frac{1}{2},$ make the left side the variable side and the right side the constant side.

Subtract $\frac{1}{2}x$ from both sides.
Combine like terms.
Subtract 5 from both sides.
Simplify.
Check: Let $x=\mathrm{-8}$ .

Solution

Since $3.4>1.6,$ make the left side the variable side and the right side the constant side.

Subtract $1.6x$ from both sides.
Combine like terms.
Subtract 4 from both sides.
Simplify.
Use the Division Property of Equality.
Simplify.
Check: Let $x=\mathrm{-5}$ .

Solution

Simplify each side of the equation as much as possible. Use the Distributive Property.
Collect all variable terms on one side of the equation—all $x$ s are already on the left side.
Collect constant terms on the other side of the equation. Subtract 6 from each side
Simplify.
Make the coefficient of the variable term equal to 1. Divide each side by 3.
Simplify.
Check: Let $x=4$ .