방정식과 부등식 전체 문제

Answers will vary.

$1$

$-\frac{8}{3}$

$-25$

We use the Division Property of Equality to divide both sides by $4.$

Divide both sides by 4 to undo the multiplication.
Simplify.
Check your answer. Let $x=-7$.

Since this is a true statement, $x=-7$ is a solution to $4x=-28.$

y = −16

z = −13

Here $a$ is divided by $-7.$ We can multiply both sides by $-7$ to isolate $a.$

Multiply both sides by $-7$.
Simplify.
Check your answer. Let $a=294$.

b = 144

c = 128

Remember $-r$ is equivalent to $-1r.$

Rewrite $-r$ as $-1r$.
Divide both sides by $-1$.
Check.
Substitute $r=-2$
Simplify.

In Solve Equations with Fractions, we saw that there are two other ways to solve $-r=2.$

We could multiply both sides by $-1.$

We could take the opposite of both sides.

k = −8

g = −3

Since the product of a number and its reciprocal is $1,$ our strategy will be to isolate $x$ by multiplying by the reciprocal of $\frac{2}{3}.$

Multiply by the reciprocal of $\frac{2}{3}$.
Reciprocals multiply to one.
Multiply.
Check your answer. Let $x=27$

Notice that we could have divided both sides of the equation $\frac{2}{3}x=18$ by $\frac{2}{3}$ to isolate $x.$ While this would work, multiplying by the reciprocal requires fewer steps.

n = 35

y = 18

Start by combining like terms to simplify each side.

Combine like terms.
Divide both sides by 12 to isolate x.
Simplify.
Check your answer. Let $x=1$

x = 2

n = −5

Simplify each side by combining like terms.

Simplify each side.
Divide both sides by 3 to isolate y.
Simplify.
Check your answer. Let $y=-3$

Notice that the variable ended up on the right side of the equal sign when we solved the equation. You may prefer to take one more step to write the solution with the variable on the left side of the equal sign.