M1 Unit 1 Review

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5

Answer explanation

In the expression 5d + 2, the coefficient is the number that multiplies the variable. Here, 5 is the coefficient of d, making it the correct answer.

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5d and 2

Answer explanation

In the expression 5d + 2, the terms are the distinct parts that are added together. Here, 5d and 2 are both separate terms, making '5d and 2' the correct choice.

Front

A letter that represents a number is called a _____.

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variable

Answer explanation

A letter that represents a number is called a variable. In mathematics, variables are used to denote unknown values, making them essential for algebraic expressions and equations.

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Back

Answer explanation

To solve for l in the equation V = lwh, divide both sides by wh. This gives l = V / (wh), which matches the correct answer choice.

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Back

Answer explanation

To solve for x in the equation ax - b = c, first add b to both sides: ax = c + b. Then, divide both sides by a to isolate x: x = (c + b) / a. Thus, the correct answer is x = (c + b) / a.

Front

An equation has ____________ when you simplify and the variable terms on each side are the same, BUT the constants are different.

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no solution

Answer explanation

An equation has no solution when the variable terms are the same on both sides, but the constants differ. This means there is no value for the variable that can satisfy the equation.

Front

An equation has ____________ when you simplify and the variable terms on each side are the same, AND the constants are the same.

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infinite solutions

Answer explanation

An equation has infinite solutions when the variable terms and constants on both sides are identical after simplification. This means any value for the variable will satisfy the equation, leading to infinitely many solutions.

Front

2(4x - 3) - 8 = 4 + 2x

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x = 3

Answer explanation

To solve 2(4x - 3) - 8 = 4 + 2x, first distribute: 8x - 6 - 8 = 4 + 2x. Simplifying gives 8x - 14 = 2x + 4. Rearranging leads to 6x = 18, so x = 3. Thus, the correct answer is x = 3.

Front

-3x + 6 = -3(x + 3)

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No solution

Answer explanation

To solve -3x + 6 = -3(x + 3), simplify the right side to get -3x - 9. This leads to 6 = -9, which is a contradiction. Therefore, there is no solution.

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3(x - 3) ≤ 2(x + 2)

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x ≤ 13

Answer explanation

To solve 3(x - 3) ≤ 2(x + 2), first distribute: 3x - 9 ≤ 2x + 4. Then, subtract 2x from both sides: x - 9 ≤ 4. Adding 9 gives x ≤ 13. Thus, the correct answer is x ≤ 13.