Solve Multi-Step Linear Equations
Solve for x: 3x + 7 = 16
Answer: x = 3
Solve for x: 2x - 5 > 7
Answer: x > 6
Solve for h in the formula A = 1/2bh
Answer: h = 2A/b
How many solutions does the equation 2x + 3 = 2x + 5 have?
Answer: Zero solutions (inconsistent)
A movie ticket costs $12. Write an equation to find the total cost C for n tickets.
Answer: C = 12n
Solve for x: 4(x - 3) = 2x + 6
Answer: x = 9
Solve for x: 3(x + 2) ≤ 5x - 4
Answer: x ≥ 5
Solve for r in the formula I = Prt
Answer: r = I/(Pt)
How many solutions does the equation 3(2x - 4) = 6x - 12 have?
Answer: Infinitely many solutions (identity)
A phone plan costs $25 per month plus $0.10 per text message. Write an equation for the monthly cost C when sending m messages.
Answer: C = 25 + 0.10m
Solve for x: (x + 5)/3 - (x - 2)/2 = 4
Answer: x = 6
Solve for x: (x - 3)/4 + 2 ≥ (x + 1)/2
Answer: x ≤ 5
Solve for h in the formula V = πr²h
Answer: h = V/(πr²)
How many solutions does the equation 2(3x - 1) - 5x = x + 4 have?
Answer: One solution (x = -6)
A taxi charges $3.50 for the first mile and $2.75 for each additional mile. Write an equation for the cost C of a ride that is m miles (where m ≥ 1).
Answer: C = 3.50 + 2.75(m - 1) or C = 0.75 + 2.75m
Solve for x: 2.5(x + 4) - 1.2x = 3.8x - 7.5
Answer: x = -3
Solve for x: 4/5(x - 2) + 3 < 2/3(x + 1) - 1
Answer: x > 31
Solve for c in the Pythagorean theorem: a² + b² = c²
Answer: c = √(a² + b²)
Determine the value of k for which the equation 3x - 5 = kx + 7 has no solutions.
Answer: k = 3
A rectangular garden has a perimeter of 30 feet. Write an equation relating the length l and width w.
Answer: 2l + 2w = 30 or l + w = 15
Solve for x: |3x - 4| + 2 = 11
Answer: x = 3 or x = -1
Solve for x: |2x - 5| ≤ 3
Answer: 1 ≤ x ≤ 4
Solve for x₂ in the point-slope form: (y - y₁) = m(x - x₁)
Answer: x₂ = (y₂ - y₁)/m + x₁
For what values of k will the equation (k-2)x + 3 = kx - 5 have exactly one solution?
Answer: All values of k except k = 2
A company manufactures calculators. The fixed cost is $5000 and each calculator costs $12 to make. If the company sells each calculator for $20, write an equation for the profit P after selling n calculators.
Answer: P = 20n - (5000 + 12n) or P = 8n - 5000