7th Grade Algebra Flashcard

Front

Expand the algebraic expression: 5(3f+4)

Back

15f+20

Answer explanation

To expand 5(3f+4), distribute 5 to both terms: 5*3f = 15f and 5*4 = 20. Thus, the expression becomes 15f + 20, which matches the correct answer choice.

Front

Expand the algebraic expression: 4(4g-3)

Back

16g-12

Answer explanation

To expand 4(4g-3), distribute 4: 4 * 4g = 16g and 4 * -3 = -12. Thus, the expression becomes 16g - 12. Since this is not among the answer choices, the correct answer is 'None of the above'.

Front

Expand the algebraic expression: 0.5(18z - 1.5)

Back

9z - 0.75

Answer explanation

To expand 0.5(18z - 1.5), distribute 0.5: 0.5 * 18z = 9z and 0.5 * -1.5 = -0.75. Thus, the expression simplifies to 9z - 0.75, which matches the correct answer choice.

Front

Simplify the algebraic expression: 6 + 7(5 - n)

Back

41 - 7n

Answer explanation

To simplify 6 + 7(5 - n), first distribute 7: 6 + 35 - 7n. Then combine like terms: 6 + 35 = 41, resulting in 41 - 7n. Thus, the correct answer is 41 - 7n.

Front

Expand the algebraic expression: 6(d + 2)

Back

6d + 12

Answer explanation

To expand 6(d + 2), distribute 6 to both terms inside the parentheses: 6 * d + 6 * 2 = 6d + 12. Thus, the correct answer is 6d + 12.

Front

Simplify the algebraic expression:
4(3d)²

Back

None of the above

Answer explanation

To simplify 4(3d)², first calculate (3d)² = 9d². Then multiply by 4: 4 * 9d² = 36d². Since 36d² is not listed, the correct answer is 'None of the above'.

Front

Which operation is NOT appropriate to solve the equation: 3y=17? Options: Subtract 2y from both sides, Divide both sides by 3, Multiply both sides by one third, All three methods are appropriate.

Back

Subtract 2y from both sides

Answer explanation

Subtracting 2y from both sides is inappropriate because it changes the variable's coefficient, making it impossible to isolate y. The other operations correctly manipulate the equation to solve for y.

Front

Which operation is appropriate to solve the equation: f² = 196?

Back

Take the square root of both sides

Answer explanation

To solve f² = 196, taking the square root of both sides is appropriate. This gives f = ±14, which directly addresses the equation. Dividing by f or 196 does not isolate f correctly.

Front

Which operation is NOT an appropriate step to solve the equation: 5y + 3 = 17 - 2y?

Back

Add 17 to both sides

Answer explanation

Adding 17 to both sides is not appropriate because it would change the equation's balance. The correct steps involve isolating y by adding 2y or subtracting 3, but not adding 17.

Front

Which of the following expressions are not equivalent? 3t + 17 - t - 1, 2(t + 8), t² + 2t + 2 x 8 - t², 4t + 16 - 2t + 2

Back

4t + 16 - 2t + 2

Answer explanation

The expression '4t + 16 - 2t + 2' simplifies to '2t + 18', which is not equivalent to the others. The other expressions simplify to '2t + 16', '2t + 16', and '2t + 16' respectively.