Multi-Step Equations
Solve: 3x+5=20
x = 5
Solve: x+7>12
x > 5
Solve: −2 < x + 3 < 6
−5 < x < 3
Solve A=1/2bh for h.
h=2A/b
Why does this equation have infinitely many solutions?
12x+32/4=3x+8
The equation above has infinitely many solutions because both sides simplify to the same expression.
Solve: 4x−7=21
x = 7
Solve: 3x −4 ≤11
x ≤ 5
Solve: −12 < 3x < 9
−4 < x < 3
Solve p=4r+3t for r.
r=p−3t/4
What is the first step to solve:
y/3=6+x
Multiply both sides by 3.
Solve: 3(2x−1)=2x+1
x = 1
Solve: 7x + 10 − 11x ≤ 2
x ≥ 2
Solve: −36 < 3x − 6 < −15
−10 < x < −3
A triangle has an area of 252 square feet and a base of 24 feet. Find the height.
h=21 feet
What happens when you multiply or divide an inequality by a negative number?
Reverse (flip) the inequality sign.
Solve: 5(x+2)−3=2x+15
x = 8/3
Solve: 4x − 25 > 9x + 5
x < −6
Solve: x − 4 <−10x - 4 < -10 OR 2x > 3
x < −6x < -6 OR x > 6
Solve Ax+By=C for B.
B=C−Ax /y
A shelter had fewer than 27 dogs and ended the month with 14 dogs. Write an inequality for the number of dogs adopted, xx.
x < 13
Solve: 2(3x−4)+5=4x+9
x = 6
Solve: −5x + 8 ≥ 23
x ≤ −3
Solve: 2x + 1 ≤−72x + 1 > -7 OR 3x − 6 > 9
x ≤ −4 OR x > 5
A triangle has an area of 180 square feet and a base of 20 feet. Find the height.
h=18 feet
Explain why 2 is included in x ≥ 2.
The symbol ≥ means greater than or equal to, so 2 is included.