example 1 collecting like terms x + 2 = 3x x + 2 –x = 3x – x 2 = 2x 1 = x original equation...
TRANSCRIPT
EXAMPLE 1 Collecting Like Terms
x + 2 = 3x
x + 2 –x = 3x – x
2 = 2x
1 = x
Original equation
Subtract x from each side.
Divide both sides by 2.
22
2x2=
EXAMPLE 2 Solve a Multi-Step Problem
Each side of the triangle has the same length. What is the perimeter of the triangle?
SOLUTION
5x + 9 = 7x + 5 Write an equation.
5x + 9 –5x = 7x + 5 –5x Subtract 5x from each side.
9 = 2x + 5 Simplify.
9 –5 = 2x + 5–5 Subtract 5 from each side.
4 = 2x Simplify.42
2x2= Divide each side by 2
2 = x Simplify.
EXAMPLE 2 Solve a Multi-Step Problem
Because 5x + 9 = 5(2) + 9 = 19, each side of the triangle is 19 units long. Since each side of the triangle has the same length, the perimeter is 3 19, or 57 units.
The perimeter of the triangle is 57 units.
ANSWER
EXAMPLE 3 Using the Distributive Property
21x = 3(2x + 30) Original equation.
21x –6x = 6x + 90 –6x Subtract 6x from each side.
15x = 90 Simplify.
Divide each side by 15
x = 6 Simplify.
21x = 6x + 90 Distributive property
1515x15
90=
GUIDED PRACTICE for Examples 1, 2, and 3
55 + 3x = 8x1.
11 = x
Solve the equation.
GUIDED PRACTICE for Examples 1, 2, and 3
9x = 12x – 92.
x = 3
GUIDED PRACTICE for Examples 1, 2, and 3
–15x + 120 = 15x3.
4 = x
GUIDED PRACTICE for Examples 1, 2, and 3
4. 4a + 5 = a + 11
2 = a
GUIDED PRACTICE for Examples 1, 2, and 3
n = –8
3n + 7 = 2n –15.
GUIDED PRACTICE for Examples 1, 2, and 3
–6c + 1 = –9c + 76.
c = 2
GUIDED PRACTICE for Examples 1, 2, and 3
5 = s
28 –3s = 5s –127.
GUIDED PRACTICE for Examples 1, 2, and 3
w = –18
4(w – 9) = 7w + 188.
GUIDED PRACTICE for Examples 1, 2, and 3
y = –3
9. 2(y + 4) = –3y – 7