8.4 Solve Equations with Fraction or Decimal Coefficients

Before you get started, take this readiness quiz.

Multiply: $8 \cdot \frac{3}{8} .$
If you missed this problem, review the reference

Find the LCD of $\frac{5}{6} \text{and} \frac{1}{4} .$
If you missed this problem, review the reference

Multiply: $4.78$ by $100 .$
If you missed this problem, review the reference

Solve: $\frac{1}{4} x + \frac{1}{2} = \frac{5}{8} .$

Solve: $\frac{1}{6} y - \frac{1}{3} = \frac{1}{6} .$

Solve: $6 = \frac{1}{2} v + \frac{2}{5} v - \frac{3}{4} v .$

Solve: $−1 = \frac{1}{2} u + \frac{1}{4} u - \frac{2}{3} u .$

Solve: $a + \frac{3}{4} = \frac{3}{8} a - \frac{1}{2} .$

Solve: $c + \frac{3}{4} = \frac{1}{2} c - \frac{1}{4} .$

Solve: $−11 = \frac{1}{2} \left(6 p + 2\right) .$

Solve: $8 = \frac{1}{3} \left(9 q + 6\right) .$

Solve: $\frac{1}{5} \left(n + 3\right) = \frac{1}{4} \left(n + 2\right) .$

Solve: $\frac{1}{2} \left(m - 3\right) = \frac{1}{4} \left(m - 7\right) .$

Solve: $0.6 x - 1 = 11 .$

Solve: $1.2 x - 3 = 9 .$

Solve: $0.14 h + 0.12 = 0.35 h - 2.4 .$

Solve: $0.65 k - 0.1 = 0.4 k - 0.35 .$

Solve: $0.25 n + 0.05 \left(n + 5\right) = 2.95 .$

Solve: $0.10 d + 0.05 \left(d - 5\right) = 2.15 .$

Solve the equation by clearing the fractions.

$\frac{1}{4} x - \frac{1}{2} = - \frac{3}{4}$

Solve the equation by clearing the fractions.

$\frac{5}{6} y - \frac{2}{3} = - \frac{3}{2}$

Solve the equation by clearing the fractions.

$\frac{1}{2} a + \frac{3}{8} = \frac{3}{4}$

Solve the equation by clearing the fractions.

$2 = \frac{1}{3} x - \frac{1}{2} x + \frac{2}{3} x$

Solve the equation by clearing the fractions.

$\frac{1}{4} m - \frac{4}{5} m + \frac{1}{2} m = −1$

Solve the equation by clearing the fractions.

$x + \frac{1}{2} = \frac{2}{3} x - \frac{1}{2}$

Solve the equation by clearing the fractions.

$\frac{1}{3} w + \frac{5}{4} = w - \frac{1}{4}$

Solve the equation by clearing the fractions.

$\frac{1}{2} x - \frac{1}{4} = \frac{1}{12} x + \frac{1}{6}$

Solve the equation by clearing the fractions.

$\frac{1}{3} b + \frac{1}{5} = \frac{2}{5} b - \frac{3}{5}$

Solve the equation by clearing the fractions.

$1 = \frac{1}{6} \left(12 x - 6\right)$

Solve the equation by clearing the fractions.

$\frac{1}{4} \left(p - 7\right) = \frac{1}{3} \left(p + 5\right)$

Solve the equation by clearing the fractions.

$\frac{1}{2} \left(x + 4\right) = \frac{3}{4}$

Solve the equation by clearing the decimals.

$0.6 y + 3 = 9$

Solve the equation by clearing the decimals.

$3.6 j - 2 = 5.2$

Solve the equation by clearing the decimals.

$0.4 x + 0.6 = 0.5 x - 1.2$

Solve the equation by clearing the decimals.

$0.23 x + 1.47 = 0.37 x - 1.05$

Solve the equation by clearing the decimals.

$0.9 x - 1.25 = 0.75 x + 1.75$

Solve the equation by clearing the decimals.

$0.05 n + 0.10 \left(n + 8\right) = 2.15$

Solve the equation by clearing the decimals.

$0.10 d + 0.25 \left(d + 5\right) = 4.05$

Solve the equation by clearing the decimals.

$0.05 \left(q - 5\right) + 0.25 q = 3.05$

Coins Taylor has $\$\text{2}.\text{00}$ in dimes and pennies. The number of pennies is $2$ more than the number of dimes. Solve the equation $0.10 d + 0.01 \left(d + 2\right) = 2$ for $d ,$ the number of dimes.

Explain how to find the least common denominator of $\frac{3}{8} , \frac{1}{6} , \text{and} \frac{2}{3} .$

If an equation has fractions only on one side, why do you have to multiply both sides of the equation by the LCD?

Determine whether the given number is a solution to the equation.

$x + 16 = 31 , x = 15$

Determine whether the given number is a solution to the equation.

$−9 n = 45 , n = 54$

Solve the equation using the Subtraction Property of Equality.

$x + 7 = 19$

Solve the equation using the Subtraction Property of Equality.

$a + \frac{1}{3} = \frac{5}{3}$

Solve the equation using the Addition Property of Equality.

$u - 7 = 10$

Solve the equation using the Addition Property of Equality.

$c - \frac{3}{11} = \frac{9}{11}$

Solve the equation.

$n - 12 = 32$

Solve the equation.

$f + \frac{2}{3} = 4$

Solve the equation.

$y + 8 - 15 = −3$

Solve the equation.

$6 \left(n - 1\right) - 5 n = −14$

Translate each English sentence into an algebraic equation and then solve it.

The sum of $−6$ and $m$ is $25 .$

Translate into an algebraic equation and solve.

Rochelle’s daughter is $11$ years old. Her son is $3$ years younger. How old is her son?

Translate into an algebraic equation and solve.

Peter paid $\$\text{9}.\text{75}$ to go to the movies, which was $\$\text{46}.\text{25}$ less than he paid to go to a concert. How much did he pay for the concert?

Solve each equation using the Division Property of Equality.

$8 x = 72$

Solve each equation using the Division Property of Equality.

$0.25 p = 5.25$

Solve each equation using the Multiplication Property of Equality.

$\frac{n}{6} = 18$

Solve each equation using the Multiplication Property of Equality.

$36 = \frac{3}{4} x$

Solve each equation.

$−18 m = −72$

Solve each equation.

$0.45 x = 6.75$

Solve each equation.

$5 r - 3 r + 9 r = 35 - 2$

Solve the equations with constants on both sides.

$8 p + 7 = 47$

Solve the equations with constants on both sides.

$3 x + 19 = −47$

Solve the equations with variables on both sides.

$7 y = 6 y - 13$

Solve the equations with variables on both sides.

$k = −6 k - 35$

Solve the equations with constants and variables on both sides.

$12 x - 9 = 3 x + 45$

Solve the equations with constants and variables on both sides.

$4 u + 16 = −19 - u$

Solve each linear equation using the general strategy.

$6 \left(x + 6\right) = 24$

Solve each linear equation using the general strategy.

$- \left(s + 4\right) = 18$

Solve each linear equation using the general strategy.

$23 - 3 \left(y - 7\right) = 8$

Solve each linear equation using the general strategy.

$8 \left(r - 2\right) = 6 \left(r + 10\right)$

Solve each linear equation using the general strategy.

$4 \left(3.5 y + 0.25\right) = 365$

Solve each equation by clearing the fractions.

$\frac{2}{5} n - \frac{1}{10} = \frac{7}{10}$

Solve each equation by clearing the fractions.

$\frac{3}{4} a - \frac{1}{3} = \frac{1}{2} a + \frac{5}{6}$

Solve each equation by clearing the decimals.

$0.8 x - 0.3 = 0.7 x + 0.2$

Solve each equation by clearing the decimals.

$0.6 p - 1.9 = 0.78 p + 1.7$

Determine whether each number is a solution to the equation.
$3 x + 5 = 23 .$

1. ⓐ $6$
2. ⓑ $\frac{23}{5}$

Solve each equation.

$9 c = 144$

Solve each equation.

$−8 x - 15 + 9 x - 1 = −21$

Solve each equation.

$\frac{2}{3} x = 6$

Solve each equation.

$10 y = −5 y + 60$

Solve each equation.

$9 m - 2 - 4 m + m = 42 - 8$

Solve each equation.

$- \left(d + 9\right) = 23$

Solve each equation.

$2 \left(6 x + 5\right) - 8 = −22$

Solve each equation.

$\frac{1}{4} p + \frac{1}{3} = \frac{1}{2}$

Solve each equation.

Translate and solve: The difference of twice $x$ and $4$ is $16 .$