Select the correct answer from each drop-down menu.
Consider the equation below.
[tex]$-2(5 x+8)=14+6 x$[/tex]
The equation was solved using the following steps.
Step 1: [tex]$-10 x-16=14+6 x$[/tex]
Step 2: [tex]$-16 x-16=14$[/tex]
Step 3: [tex]$-16 x=30$[/tex]
Step 4: [tex]$x=\frac{30}{-16}$[/tex]
Step 5: [tex]$x=-\frac{15}{8}$[/tex]
Complete the statements below with the process used to achieve steps 1-4.
Step 1: [ ] -2 to [tex]$5 x$[/tex] and 8.
Step 2: [ ] [tex]$6 x$[/tex].
Step 3: [ ] 16.
Step 4: [ ] -16.
Answer (1)
Step 1: Distribute -2 to 5 x and 8.
Step 2: Subtract 6 x .
Step 3: Add 16.
Step 4: Divide by -16.
Explanation
Problem Analysis We are given the equation − 2 ( 5 x + 8 ) = 14 + 6 x and the steps taken to solve it. Our goal is to identify the operations performed in each step.
Step 1: Distributing -2 Step 1: − 10 x − 16 = 14 + 6 x . To get from − 2 ( 5 x + 8 ) to − 10 x − 16 , we distribute the -2 to both terms inside the parentheses: − 2 ∗ 5 x = − 10 x and − 2 ∗ 8 = − 16 .
Step 2: Subtracting 6x Step 2: − 16 x − 16 = 14 . To get from − 10 x − 16 = 14 + 6 x to − 16 x − 16 = 14 , we subtract 6 x from both sides of the equation: − 10 x − 6 x = − 16 x .
Step 3: Adding 16 Step 3: − 16 x = 30 . To get from − 16 x − 16 = 14 to − 16 x = 30 , we add 16 to both sides of the equation: 14 + 16 = 30 .
Step 4: Dividing by -16 Step 4: x = − 16 30 . To get from − 16 x = 30 to x = − 16 30 , we divide both sides of the equation by -16.
Summary of Operations Therefore, the operations are: Step 1: Distribute -2 to 5 x and 8. Step 2: Subtract 6 x .
Step 3: Add 16. Step 4: Divide by -16.
Examples
Understanding how to solve equations step-by-step is crucial in many real-world scenarios. For instance, if you're managing a budget and need to figure out how much you can spend each month after accounting for fixed expenses, you'll use similar algebraic techniques. Suppose you have a total income and some fixed costs, and you want to determine the amount you can allocate to discretionary spending. By setting up an equation and solving for the unknown variable, you can effectively manage your finances and make informed decisions about your spending habits. This process ensures you stay within your budget and achieve your financial goals.
