Math Problem Statement

From the set {4, 10, 12} use substitution to determine which value of x makes the equation true.

10(x - 3) = 90

Question 2Select one:

a. none of these

b. 12

c. 10

d. 4

Question 3 Not complete Points out of 1.00 Flag question Question text From the set {21, 36, 56} use substitution to determine which value of x makes the equation true.

5(x - 20) = 180

Question 3Select one:

a. 56

b. 36

c. 21

d. none of these

Solution

Let's go step by step to solve both questions.

Question 2:

We have the equation:

10(x3)=9010(x - 3) = 90

We will check each value from the set {4,10,12}\{4, 10, 12\} by substituting them into the equation.

  1. For x=4x = 4:

10(43)=10(1)=10(not equal to 90)10(4 - 3) = 10(1) = 10 \quad \text{(not equal to 90)}

  1. For x=10x = 10:

10(103)=10(7)=70(not equal to 90)10(10 - 3) = 10(7) = 70 \quad \text{(not equal to 90)}

  1. For x=12x = 12:

10(123)=10(9)=90(equal to 90, correct!)10(12 - 3) = 10(9) = 90 \quad \text{(equal to 90, correct!)}

Answer: b. 12


Question 3:

We have the equation:

5(x20)=1805(x - 20) = 180

We will check each value from the set {21,36,56}\{21, 36, 56\} by substituting them into the equation.

  1. For x=21x = 21:

5(2120)=5(1)=5(not equal to 180)5(21 - 20) = 5(1) = 5 \quad \text{(not equal to 180)}

  1. For x=36x = 36:

5(3620)=5(16)=80(not equal to 180)5(36 - 20) = 5(16) = 80 \quad \text{(not equal to 180)}

  1. For x=56x = 56:

5(5620)=5(36)=180(equal to 180, correct!)5(56 - 20) = 5(36) = 180 \quad \text{(equal to 180, correct!)}

Answer: a. 56


Summary of answers:

  • Question 2: b. 12
  • Question 3: a. 56

Would you like further details on any of these steps, or have any questions? Here's a tip:

Tip: Always simplify the expression inside parentheses first, then apply operations outside the parentheses step by step.

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Math Problem Analysis

Mathematical Concepts

Algebra
Substitution
Linear Equations

Formulas

10(x - 3) = 90

Theorems

Substitution method for solving equations

Suitable Grade Level

Grades 7-9