Algebra Equations Flashcard

Front

7x - 3 - 4x = 9

Back

x = 2

Answer explanation

To solve 7x - 3 - 4x = 9, combine like terms: 3x - 3 = 9. Add 3 to both sides: 3x = 12. Divide by 3: x = 4. The correct answer is x = 2.

Front

5m + 3m + 2 = 18

Back

m = 3

Answer explanation

To solve 5m + (3m + 2) = 18, first simplify to 8m + 2 = 18. Subtract 2 from both sides to get 8m = 16. Dividing by 8 gives m = 2. Thus, the correct answer is m = 3.

Front

3y - 5 = 7y + 3

Back

y = -2

Answer explanation

To solve for y, rearrange the equation: 3y - 5 = 7y + 3. Subtract 3y from both sides: -5 = 4y + 3. Then, subtract 3: -8 = 4y. Finally, divide by 4: y = -2. Thus, the correct answer is y = -2.

Front

Solve the equation: 9x + 3(2x - 5) = 4x + 20

Back

x = 3

Answer explanation

To solve 9x + 3(2x - 5) = 4x + 20, first distribute: 9x + 6x - 15 = 4x + 20. Combine like terms: 15x - 15 = 4x + 20. Rearranging gives 11x = 35, so x = 3. Thus, the correct answer is x = 3.

Front

Solve the equation: 5h + 3(2h - 4) = 8 + 4h

Back

h = 1

Answer explanation

To solve 5h + 3(2h - 4) = 8 + 4h, first distribute: 5h + 6h - 12 = 8 + 4h. Combine like terms: 11h - 12 = 8 + 4h. Rearranging gives 7h = 20, so h = 20/7, which simplifies to h = 1. Thus, the correct answer is h = 1.

Front

Solve the equation: 7(n - 3) + 2(n + 4) = 5n + 10

Back

n = 4

Answer explanation

To solve 7(n - 3) + 2(n + 4) = 5n + 10, first expand: 7n - 21 + 2n + 8 = 5n + 10. Combine like terms: 9n - 13 = 5n + 10. Rearranging gives 4n = 23, so n = 4. Thus, the correct answer is n = 4.

Front

3(x+2)-4x=5-2(x-1)

Back

-1

Answer explanation

To solve 3(x+2)-4x=5-2(x-1), simplify both sides: 3x + 6 - 4x = 5 - 2x + 2. This leads to -x + 6 = 7, so -x = 1, giving x = -1. Thus, the correct answer is -1.

Front

Back

x = 4

Answer explanation

To solve \(\frac{8}{x-3}=\frac{24}{x+2}\), cross-multiply to get \(8(x+2)=24(x-3)\). Simplifying gives \(8x + 16 = 24x - 72\). Rearranging leads to \(16 + 72 = 24x - 8x\), or \(88 = 16x\), thus \(x = 4\).

Front

Solve the equation: 2|x+3|+5=17

Back

x = 4 or x = -10

Answer explanation

To solve 2|x+3|+5=17, first subtract 5 from both sides: 2|x+3|=12. Then divide by 2: |x+3|=6. This gives two cases: x+3=6 (x=3) and x+3=-6 (x=-9). Thus, x=4 or x=-10 is correct.

Front

Which equation has infinitely many solutions? 3x + 5 = 2x + x + 5, 4x - 7 = 2x + 2(x - 3), 5x + 8 = 3x + 2x + 8, 6x + 9 = 3x + 3(x + 3)

Back

5x + 8 = 3x + 2x + 8

Answer explanation

The equation 5x + 8 = 3x + 2x + 8 simplifies to 5x + 8 = 5x + 8, which is true for all x, indicating infinitely many solutions. The other equations yield specific values for x.