5.4 Solve Equations with Decimals

Before you get started, take this readiness quiz.

Evaluate $x + \frac{2}{3} \text{when} x = - \frac{1}{4} .$
If you missed this problem, review the reference.

Evaluate $15 - y$ when $y = −5 .$
If you missed this problem, review the reference.

Solve $\frac{n}{- 7} = 42 .$
If you missed this problem, review the reference.

Determine whether each value is a solution of the given equation.

$x - 0.6 = 1.3 :$ⓐ $x = 0.7$ⓑ $x = 1.9$ⓒ $x = −0.7$

Determine whether each value is a solution of the given equation.

$y - 0.4 = 1.7 :$ⓐ $y = 2.1$ⓑ $y = 1.3$ⓒ $−1.3$

Solve: $y + 2.7 = −5.3 .$

Solve: $y + 3.6 = −4.8 .$

Solve: $a - 3.93 = −2.86 .$

Solve: $n - 3.47 = −2.64 .$

Solve: $−8.4 = 0.7 b .$

Solve: $−5.6 = 0.7 c .$

Solve: $\frac{c}{−2.6} = −4.5 .$

Solve: $\frac{b}{−1.2} = −5.4 .$

Translate and solve: The difference of $y$ and $4.9$ is $2.8 .$

Translate and solve: The difference of $z$ and $5.7$ is $3.4 .$

Translate and solve: The product of $−4.3$ and $x$ is $12.04 .$

Translate and solve: The product of $−3.1$ and $m$ is $26.66 .$

Translate and solve: The quotient of $q$ and $−3.4$ is $4.5 .$

Translate and solve: The quotient of $r$ and $−2.6$ is $2.5 .$

Translate and solve: The sum of $j$ and $3.8$ is $2.6 .$

Translate and solve: The sum of $k$ and $4.7$ is $0.3 .$

Determine whether each number is a solution of the given equation.

$x - 0.8 = 2.3$
ⓐ $x = 2$ⓑ $x = −1.5$ⓒ $x = 3.1$

Determine whether each number is a solution of the given equation.

$\frac{h}{1.5} = −4.3$
ⓐ $h = 6.45$ⓑ $h = −6.45$ⓒ $h = −2.1$

Solve the equation.

$y + 2.9 = 5.7$

Solve the equation.

$f + 3.45 = 2.6$

Solve the equation.

$a + 6.2 = −1.7$

Solve the equation.

$c + 1.15 = −3.5$

Solve the equation.

$n - 2.6 = 1.8$

Solve the equation.

$x - 0.4 = −3.9$

Solve the equation.

$j - 1.82 = −6.5$

Solve the equation.

$m - 0.25 = −1.67$

Solve the equation.

$0.5 x = 3.5$

Solve the equation.

$−1.7 c = 8.5$

Solve the equation.

$−1.4 p = −4.2$

Solve the equation.

$−120 = 1.5 q$

Solve the equation.

$0.24 x = 4.8$

Solve the equation.

$−3.4 z = −9.18$

Solve the equation.

$\frac{a}{0.4} = −20$

Solve the equation.

$\frac{x}{0.7} = −0.4$

Solve the equation.

$\frac{p}{- 5} = −1.65$

Solve the equation.

$\frac{r}{- 1.2} = −6$

Solve the equation. Then check your solution.

$x - 5 = −11$

Solve the equation. Then check your solution.

$p + 8 = −2$

Solve the equation. Then check your solution.

$−4.2 m = −33.6$

Solve the equation. Then check your solution.

$q + \frac{5}{6} = \frac{1}{12}$

Solve the equation. Then check your solution.

$\frac{7}{8} m = \frac{1}{10}$

Solve the equation. Then check your solution.

$- \frac{2}{3} = y + \frac{3}{8}$

Solve the equation. Then check your solution.

$\frac{11}{20} = - f$

Solve the equation. Then check your solution.

$−4.2 a = 3.36$

Solve the equation. Then check your solution.

$r - 1.25 = −2.7$

Solve the equation. Then check your solution.

$\frac{h}{- 3} = −8$

Translate and solve.

The difference of $n$ and $1.9$ is $3.4 .$

Translate and solve.

The product of $−6.2$ and $x$ is $−4.96 .$

Translate and solve.

The quotient of $y$ and $−1.7$ is $−5 .$

Translate and solve.

The sum of $n$ and $−7.3$ is $2.4.$

Shawn bought a pair of shoes on sale for $$78$. Solve the equation $0.75 p = 78$ to find the original price of the shoes, $p .$

Think about solving the equation $1.2 y = 60 ,$ but do not actually solve it. Do you think the solution should be greater than $60$ or less than $60 ?$ Explain your reasoning. Then solve the equation to see if your thinking was correct.