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3x − 7 = 11
3x − 7 = 11
3x = 18
x = 6
5x + 3 = 18
5x = 15
x = 3
x^2 * x^3
x² · x³ = x^(2+3)
= x⁵
If f(x) = x + 4, find f(6).
f(6) = 6 + 4
= 10
A number increased by 6 is 15. Find the number.
x + 6 = 15
x = 9
(2x + 4) / 2 = 6
(2x + 4)/2 = 6
2x + 4 = 12
2x = 8
x = 4
2x - 5 = 9
2x = 14
x = 7
Simplify: (x³)²
(x³)² = x^(3×2)
= x⁶
If f(x) = 2x − 3, find f(5).
f(5) = 2(5) − 3
= 10 − 3
= 7
Twice a number minus 3 equals 11. Find the number.
2x − 3 = 11
2x = 14
x = 7
Simplify:
(2x^2y)(3xy^3)
Multiply coefficients: 2 × 3 = 6
Add exponents of x: x² · x = x³
Add exponents of y: y · y³ = y⁴
Final: 6x³y⁴
3(x − 2) = 12
x − 2 = 4
x = 6
Simplify: √49
√49 = 7
If f(x) = x² − 1, find f(4).
f(4) = 4² − 1
= 16 − 1
= 15
A number decreased by 4 is three times the number. Find the number.
x − 4 = 3x
−4 = 2x
x = −2
If f(x) = 2x² − 3x, find f(4).
f(4) = 2(4²) − 3(4)
= 2(16) − 12
= 32 − 12
= 20
(3x - 4)/2 = 5
3x − 4 = 10
3x = 14
x = 14/3
Simplify: √18
√18
= √(9 × 2)
= √9 · √2
= 3√2
If f(x) = 3x² − 2x, find f(3).
f(3) = 3(3²) − 2(3)
= 3(9) − 6
= 27 − 6
= 21
The sum of a number and twice that number is 45. Find the number.
x + 2x = 45
3x = 45
x = 15
A rectangle has perimeter 30.
The length is 2W + 3.
Find the width W.
Substitute L:
2(2W + 3) + 2W = 30
4W + 6 + 2W = 30
6W + 6 = 30
6W = 24
W = 4
Solve the system:
x + y = 8
x - y = 2
x + y = 8
x − y = 2
2x = 10
x = 5
Substitute into x + y = 8:
5 + y = 8
y = 3
Solve: x² − 9 = 0
x² − 9 = 0
x² = 9
x = ±3
If f(x) = x² − 2x + 1, find f(5).
f(5) = 5² − 2(5) + 1
= 25 − 10 + 1
= 16
One number is 5 more than another. Their sum is 25. Find the numbers.
x + x + 5 = 25
2x + 5 = 25
2x = 20
x = 10