Are you ready to take this lesson's quiz? The questions below will help you find out. Make sure you understand why each correct answer is correct — if you don't, review that part of the lesson.
Which sentence is the BEST description of how inverse operations are used when solving algebraic equations?
- Inverse operations allow you to check if a solution is true.
- You can find the inverse operation within the equation.
- You can use the inverse operation to help isolate the variable on one side of the equal sign.
- The inverse operation tells you if the equation contains integers or rational numbers.
Is \( u = 84 \) the solution to the equation \(-7 = \frac{u}{-12} \)? Explain.
- Yes; when you substitute 84 for \( u \) in the equation and simplify, a true statement is the result.
- No; you cannot divide a positive number by a negative number.
- Yes; both 84 and −12 are divisible by 7.
- No; the product of two negative numbers should be negative.
Substituting \( u = 84 \) into the equation,
\(-7 = \frac{\left(84\right)}{-12} \)
\(-7 = -7 \)
The equation is true, so \( u = 84 \) is the solution to \(-7 = \frac{u}{-12} \).
Which sentence BEST describes what operation should be performed to solve the equation \( 21 = 7 + b \)?
- Add 7 to both sides of the equation.
- Subtract 7 from both sides of the equation.
- Add 7 to the left side of the equation.
- Subtract 7 from the right side of the equation.
Solve \( \frac{p}{-8} = 3 \) for \( p \).
- \( p = -{8}{3} \)
- \( p = 11 \)
- \( p = 24 \)
- \( p = -24 \)
The operation shown in the equation with the variable is division. To solve, you should multiply both sides of the equation by −8, then simplify to find the solution. Check the solution using substitution.
\( \frac{p}{-8} = 3 \)
\( \frac{p}{-8} \bbox[yellow]{\times -8} = 3 \bbox[yellow]{\times -8} \)
\( \frac{p}{-8} \bbox[yellow]{\times -\frac{8}{1}} = 3 \bbox[yellow]{\times -8} \)
\( p = -24\)
Is the value \( k = 5\), shown on the number line below, the solution of the equation \( -7 = k - 2 \)?
A horizontal number line from −8 to 8. The value 5 is plotted.
- No; −7 = (5) − 2 does not simplify to a true statement.
- No; the numbers −7 and 2 are integers.
- Yes; the difference of two numbers is always an integer.
- Yes; values to the right of 0 on the number line are always positive.
Substitute \( k = 5\) into the given equation, and then simplify to see if the result is a true statement.
−7 = (5) − 2
−7 ≠ 3
Summary
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Questions answered incorrectly:
