Solve Equations
Solve: 2(x + 5) = 3(x − 2)
x = 16
Find the slope and y-intercept: 3x − y = 5
m = 3, b = −5
Simplify: 3x⁷y² · 9x¹²y⁴
27x¹⁹y⁶
Factor completely: x² + 4x − 32
(x + 8)(x − 4)
Simplify: √98
7√2
Solve: −6(n − 6) − 3(n − 4) = 21
n = 3
Write the equation, in slope-intercept form, of the line through (4, 2) and (−6, 12)
y = −x + 6
Simplify: (−6x³y²)²
36x⁶y⁴
Factor completely: 5x² − 19x − 4
(5x + 1)(x − 4)
Multiply and simplify: 3√2 · 8√50
240
Solve: 5 − 2(3x − 4) = 3(x + 1) − 7x
x = 5
Are these two lines parallel, perpendicular, or neither? y = −(1/2)x and −2y = x + 10
Parallel
Simplify (positive exponents only): (12p⁷q⁶)/(18p⁴q¹²)
2p³/(3q⁶)
Solve by factoring: 2x² + 5x = 3
x = 1/2 or x = −3
Divide and simplify: (6√72)/(3√8)
6
Solve for y: 3x − 2y = 4x + 6
y = −(1/2)x − 3
Write, in standard form (Ax + By = C), the equation of the line with slope 3 through the point (2, −1)
3x − y = 7
Simplify (positive exponents only): x³ · x⁵ · x⁻¹¹
1/x³
Factor completely by grouping: 6x³ − 9x² + 4x − 6
(2x − 3)(3x² + 2)
Multiply and simplify: −20√10 · 4√30
−800√3
Solve: (2x − 1)/3 − (x + 2)/4 = 1
x = 22/5
A line is perpendicular to y = −(1/2)x − 7 and passes through (1, 4). Write its equation in point-slope form, then convert to standard form.
y − 4 = 2(x − 1) → 2x − y = −2
Simplify completely (positive exponents only): (3x⁻²y⁴)² · (2x⁵y⁻³)⁻¹
9y¹¹/(2x⁹)
Factor completely: a⁴ − 81
(a − 3)(a + 3)(a² + 9)
Simplify completely: 3√20 − √125 + 2√45
7√5