방정식과 부등식 전체 문제

n = 10

c = 1

The only constant, $-8,$ is on the left side of the equation and variable, $y,$ is on both sides. Let’s leave the constant on the left and collect the variables to the right.

Subtract $5y$ from both sides.
Simplify.
We have the variables on the right and the constants on the left. Divide both sides by 2.
Simplify.
Rewrite with the variable on the left.
Check: Let $y=-4$.

p = −7

m = −3

The only constant, $24,$ is on the right, so let the left side be the variable side.

Remove the $-x$ from the right side by adding $x$ to both sides.
Simplify.
All the variables are on the left and the constants are on the right. Divide both sides by 8.
Simplify.
Check: Substitute $x=3$.

j = 2

h = 1

Start by choosing which side will be the variable side and which side will be the constant side. The variable terms are $7x$ and $6x.$ Since $7$ is greater than $6,$ make the left side the variable side and so the right side will be the constant side.

Collect the variable terms to the left side by subtracting $6x$ from both sides.
Simplify.
Now, collect the constants to the right side by subtracting 5 from both sides.
Simplify.
The solution is $x=-3$.
Check: Let $x=-3$.

x = −1

y = 4

We have $6n$ on the left and $-3n$ on the right. Since $6>-3,$ make the left side the “variable” side.

We don't want variables on the right side—add $3n$ to both sides to leave only constants on the right.
Combine like terms.
We don't want any constants on the left side, so add 2 to both sides.
Simplify.
The variable term is on the left and the constant term is on the right. To get the coefficient of $n$ to be one, divide both sides by 9.
Simplify.
Check: Substitute 1 for $n$.

q = 1

n = 1

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 $a=-5$.

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!

a = −5

k = −6

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 $x=-8$.

x = 10

y = −3