Page 154 - Math Course 1 (Book 1)

Equations with Variables

Mo. 5

Lesson 1

Solve 7x + 3 = 2x + 23.

7x + 3 = 2x + 23 Write the equation.
KEY CONCEPTS: 7x – 2x + 3 =2x – 2x + 23 Subtract 2x from each
1. Solve equations with variables on side.
each side.
5x + 3 = 23 Simplify

5x + 3 – 3 = 23 – 3 Subtract 3 from each
MO. 5 - L1a side.

Solving Equations with 5x = 20 Simplify.
Variables x = 4 Check your solution.

Answer The solution is 4.
Let’s Begin

Solve 1.7 + a = 3.8a – 5.3.
Equations with Variables on 1.7 + a = 3.8a – 5.3 Write the equation.
Each Side
1.7 + a – a = 3.8a – a – 5.3 Subtract a from each
Examples side.

Solve 5x + 12 = 2x. Check your solution. 1.7 = 2.8a – 5.3 Simplify.

5x + 12 = 2x Write the equation. 1.7 + 5.3 = 2.8a – 5.3 + 5.3 Add 5.3 to each
side.
5x – 5x + 12 = 2x – 5x Subtract 5x from each side.
7.0 = 2.8a Simplify.
12 = –3x Simplify.
7.0 = 2.8a Divide each side by
–4 = x Mentally divide each side 2.8 2.8 2.8.
by –3.
2.5 = a Check your solution.
Subtract 5x from Subtract 5x from
the left side of the right side of
the equation the equation to Answer The solution is 2.5
to isolate the keep it balanced
variable.
To check your solution, replace x with –4 in the REAL WORLD EXAMPLE
original equation.
CAR RENTAL
Check 5x + 12 = 2x Write the equation.
A car rental agency has two plans. Under plan A,
?
5(–4) + 12 = 2(–4) Replace x with –4. a car rents for $80 plus $20 each day. Under plan
B, a car rents for $120 plus $15 each day. What
?
–20 + 12 = –8 Simplify. number of days results in the same cost?
–8 = –8 This statement is
true.

Answer The solution is –4.

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