Question

steps:

1. get variables on the same side of the equal sign by applying the opposite operation to both sides of the equation.
2. combine like terms
3. now you should have a two step equation
4. solve
5. check answer

examples:

1. $3x - 5 = 2x + 7$
2. $6 - 4x = 12 + 2x$
3. $10 - 5x = 5x - 20$
4. $7x - 10 = 4x + 5$
5. $12 - 12x = -6x + 48$
6. $-11x + 21 = -3x - 3$

Explanation:

Example 1: $3x - 5 = 2x + 7$

Step1: Move variables to left side

Subtract $2x$ from both sides:
$3x - 2x - 5 = 2x - 2x + 7$

Step2: Combine like terms

$x - 5 = 7$

Step3: Isolate the variable

Add 5 to both sides:
$x - 5 + 5 = 7 + 5$

Step4: Check answer

Substitute $x=12$ into original equation:
$3(12)-5=31$, $2(12)+7=31$; $31=31$

Example 2: $6 - 4x = 12 + 2x$

Step1: Move variables to left side

Subtract $2x$ from both sides:
$6 - 4x - 2x = 12 + 2x - 2x$

Step2: Combine like terms

$6 - 6x = 12$

Step3: Isolate the variable term

Subtract 6 from both sides:
$6 - 6 - 6x = 12 - 6$
$-6x = 6$
Divide by $-6$:
$x = \frac{6}{-6}$

Step4: Check answer

Substitute $x=-1$ into original equation:
$6-4(-1)=10$, $12+2(-1)=10$; $10=10$

Example 3: $10 - 5x = 5x - 20$

Step1: Move variables to left side

Subtract $5x$ from both sides:
$10 - 5x - 5x = 5x - 5x - 20$

Step2: Combine like terms

$10 - 10x = -20$

Step3: Isolate the variable term

Subtract 10 from both sides:
$10 - 10 - 10x = -20 - 10$
$-10x = -30$
Divide by $-10$:
$x = \frac{-30}{-10}$

Step4: Check answer

Substitute $x=3$ into original equation:
$10-5(3)=-5$, $5(3)-20=-5$; $-5=-5$

Example 4: $7x - 10 = 4x + 5$

Step1: Move variables to left side

Subtract $4x$ from both sides:
$7x - 4x - 10 = 4x - 4x + 5$

Step2: Combine like terms

$3x - 10 = 5$

Step3: Isolate the variable

Add 10 to both sides:
$3x - 10 + 10 = 5 + 10$
$3x = 15$
Divide by 3:
$x = \frac{15}{3}$

Step4: Check answer

Substitute $x=5$ into original equation:
$7(5)-10=25$, $4(5)+5=25$; $25=25$

Example 5: $12 - 12x = -6x + 48$

Step1: Move variables to left side

Add $6x$ to both sides:
$12 - 12x + 6x = -6x + 6x + 48$

Step2: Combine like terms

$12 - 6x = 48$

Step3: Isolate the variable term

Subtract 12 from both sides:
$12 - 12 - 6x = 48 - 12$
$-6x = 36$
Divide by $-6$:
$x = \frac{36}{-6}$

Step4: Check answer

Substitute $x=-6$ into original equation:
$12-12(-6)=84$, $-6(-6)+48=84$; $84=84$

Example 6: $-11x + 21 = -3x - 3$

Step1: Move variables to left side

Add $3x$ to both sides:
$-11x + 3x + 21 = -3x + 3x - 3$

Step2: Combine like terms

$-8x + 21 = -3$

Step3: Isolate the variable term

Subtract 21 from both sides:
$-8x + 21 - 21 = -3 - 21$
$-8x = -24$
Divide by $-8$:
$x = \frac{-24}{-8}$

Step4: Check answer

Substitute $x=3$ into original equation:
$-11(3)+21=-12$, $-3(3)-3=-12$; $-12=-12$

Answer:

1. $x=12$
2. $x=-1$
3. $x=3$
4. $x=5$
5. $x=-6$
6. $x=3$