Algebra Equations

Cards · 52

2x + 5 = 15

Subtract 5 from both sides to get 2x = 10. Divide both sides by 2 to get x = 5.

3x - 7 = 14

Add 7 to both sides to get 3x = 21. Divide both sides by 3 to get x = 7.

5x + 12 = 2

Subtract 12 from both sides to get 5x = -10. Divide both sides by 5 to get x = -2.

4x - 9 = -1

Add 9 to both sides to get 4x = 8. Divide both sides by 4 to get x = 2.

7x - 3 = 4x + 9

Subtract 4x from both sides to get 3x - 3 = 9. Add 3 to get 3x = 12. Divide by 3 to get x = 4.

2(x + 4) = 18

Distribute 2 to get 2x + 8 = 18. Subtract 8 to get 2x = 10. Divide by 2 to get x = 5.

5(2x - 3) = 25

Divide by 5 to get 2x - 3 = 5. Add 3 to get 2x = 8. Divide by 2 to get x = 4.

x / 4 + 3 = 7

Subtract 3 from both sides to get x / 4 = 4. Multiply both sides by 4 to get x = 16.

(2x + 1) / 3 = 5

Multiply both sides by 3 to get 2x + 1 = 15. Subtract 1 to get 2x = 14. Divide by 2 to get x = 7.

x^2 - 16 = 0

Add 16 to both sides to get x^2 = 16. Take the square root of both sides to get x = 4 or x = -4.

x^2 - 5x + 6 = 0

Factor as (x - 2)(x - 3) = 0. Set each factor to zero to find x = 2 and x = 3.

x^2 + 7x + 12 = 0

Factor as (x + 3)(x + 4) = 0. Set each factor to zero to find x = -3 and x = -4.

x^2 - 4x - 5 = 0

Factor as (x - 5)(x + 1) = 0. Set each factor to zero to find x = 5 and x = -1.

2x^2 + 5x - 3 = 0

Factor as (2x - 1)(x + 3) = 0. Set each factor to zero to find x = 1/2 and x = -3.

x^2 - 6x + 9 = 0

Factor as the perfect square (x - 3)^2 = 0. Take the square root to get x = 3.

x^2 + 2x - 8 = 0 by completing the square

Rewrite as x^2 + 2x = 8. Add 1 to both sides: (x + 1)^2 = 9. Take square roots: x + 1 = ±3, so x = 2 or x = -4.

x^2 - 4x + 1 = 0

Use the quadratic formula with a=1, b=-4, c=1: x = (4 ± √(16 - 4)) / 2 = (4 ± √12) / 2 = 2 ± √3.

3x^2 = 27

Divide both sides by 3 to get x^2 = 9. Take the square root of both sides to find x = 3 or x = -3.

|x - 4| = 7

Split into two cases: x - 4 = 7 or x - 4 = -7. Solve each to get x = 11 or x = -3.

|2x + 3| = 9

Split into 2x + 3 = 9 and 2x + 3 = -9. Solve to get 2x = 6 (x = 3) or 2x = -12 (x = -6).

3|x| - 5 = 10

Add 5 to get 3|x| = 15. Divide by 3 to get |x| = 5. Therefore, x = 5 or x = -5.

√(x + 3) = 5

Square both sides to get x + 3 = 25. Subtract 3 from both sides to find x = 22.

√(2x - 1) = 3

Square both sides to get 2x - 1 = 9. Add 1 to get 2x = 10. Divide by 2 to get x = 5.

√(x + 7) = x + 1

Square both sides: x + 7 = x^2 + 2x + 1. Rearrange to x^2 + x - 6 = 0, factor as (x + 3)(x - 2) = 0. Check solutions: x = 2 (x = -3 is extraneous).

1/x + 1/2 = 3/4

Subtract 1/2 from both sides to get 1/x = 1/4. Invert both sides to obtain x = 4.

3 / (x - 2) = 1

Multiply both sides by x - 2 to get 3 = x - 2. Add 2 to both sides to find x = 5.

2 / x = 6 / (x + 8)

Cross-multiply to get 2(x + 8) = 6x, so 2x + 16 = 6x. Subtract 2x to get 4x = 16, hence x = 4.

(x + 1) / (x - 1) = 3

Multiply by x - 1 to get x + 1 = 3x - 3. Subtract x and add 3 to get 2x = 4, so x = 2.

2^x = 16

Rewrite 16 as a power of 2: 2^x = 2^4. Equate exponents to get x = 4.

3^(x + 1) = 27

Rewrite 27 as 3^3: 3^(x + 1) = 3^3. Equate exponents to get x + 1 = 3, so x = 2.

5^(2x - 1) = 125

Rewrite 125 as 5^3: 2x - 1 = 3. Add 1 to get 2x = 4. Divide by 2 to find x = 2.

4^x = 8

Express with base 2: (2^2)^x = 2^3, so 2^(2x) = 2^3. Equate exponents: 2x = 3, giving x = 3/2.

log2(x) = 5

Convert to exponential form: x = 2^5. Compute the power to get x = 32.

log3(2x - 1) = 2

Convert to exponential form: 2x - 1 = 3^2 = 9. Add 1 to get 2x = 10. Divide by 2 to find x = 5.

ln(x) = 3

Convert to exponential form with base e: x = e^3.

log(x) + log(4) = 2

Combine logarithms: log(4x) = 2. Convert from base 10: 4x = 10^2 = 100. Divide by 4 to get x = 25.

x^3 - 8 = 0

Factor as difference of cubes: (x - 2)(x^2 + 2x + 4) = 0. The real solution is x = 2.

x^3 - 4x = 0

Factor out x: x(x^2 - 4) = 0. Factor difference of squares: x(x - 2)(x + 2) = 0. Roots are x = 0, 2, and -2.

x^4 - 5x^2 + 4 = 0

Let u = x^2: u^2 - 5u + 4 = 0, factoring as (u - 1)(u - 4) = 0. Thus x^2 = 1 or x^2 = 4, so x = ±1 or ±2.

x^3 + 2x^2 - x - 2 = 0

Factor by grouping: x^2(x + 2) - 1(x + 2) = 0, giving (x^2 - 1)(x + 2) = 0. Roots are x = 1, -1, and -2.

System: x + y = 6, x - y = 2

Add both equations: 2x = 8, so x = 4. Substitute into the first equation: 4 + y = 6, so y = 2.

System: 2x + y = 7, y = 3x - 3

Substitute y: 2x + (3x - 3) = 7. Combine: 5x = 10, so x = 2. Plug back in: y = 3(2) - 3 = 3.

System: 3x + 2y = 12, 5x - 2y = 4

Add the equations to eliminate y: 8x = 16, so x = 2. Substitute: 3(2) + 2y = 12, 2y = 6, so y = 3.

x^2 + 6x = 0

Factor out x to get x(x + 6) = 0. Set each factor to zero to find x = 0 and x = -6.

4x^2 - 25 = 0

Factor difference of squares: (2x - 5)(2x + 5) = 0. Solve each factor to find x = 5/2 and x = -5/2.

x/3 + x/6 = 3

Multiply the entire equation by 6: 2x + x = 18. Combine terms: 3x = 18. Divide by 3 to get x = 6.

10 - 3x = 4x - 11

Add 3x to both sides: 10 = 7x - 11. Add 11: 21 = 7x. Divide by 7 to get x = 3.

log2(x + 3) - log2(x) = 1

Use quotient rule: log2((x + 3)/x) = 1. Convert to exponential: (x + 3)/x = 2. Solve x + 3 = 2x to get x = 3.

e^(2x) = 7

Take the natural logarithm of both sides: 2x = ln(7). Divide by 2 to get x = ln(7) / 2.

(x - 3)^2 = 16

Take the square root of both sides: x - 3 = ±4. Solve both: x = 3 + 4 = 7 or x = 3 - 4 = -1.

2 / (x + 1) = 4 / (3x - 1)

Cross-multiply: 2(3x - 1) = 4(x + 1). Expand: 6x - 2 = 4x + 4. Simplify: 2x = 6, yielding x = 3.

x^2 + 10x + 25 = 0

Factor as the perfect square trinomial (x + 5)^2 = 0. Take the square root to find x = -5.