Marlena solved the equation $2 x+5=-10-x$. Her steps are shown below.
$2 x+5=-10-x$
1. $3 x+5=-10$
2. $3 x=-15$
3. $x=-5$
Use the drop-down menus to justify Marlena's work in each step of the process.
Step 1: $\square$
Step 2: $\square$
Step 3: $\square$
Answer (1)
In Step 1, x is added to both sides of the equation: 2 x + 5 + x = − 10 − x + x , resulting in 3 x + 5 = − 10 .
In Step 2, 5 is subtracted from both sides: 3 x + 5 − 5 = − 10 − 5 , which simplifies to 3 x = − 15 .
In Step 3, both sides are divided by 3: 3 3 x = 3 − 15 , leading to the solution x = − 5 .
The solution to the equation is x = − 5 .
Explanation
Understanding the Problem The problem is to justify the steps Marlena took to solve the equation 2 x + 5 = − 10 − x . We need to identify the operation performed in each step to transform the equation into its next equivalent form.
Justifying Step 1 Step 1: From 2 x + 5 = − 10 − x to 3 x + 5 = − 10 , we observe that x was added to both sides of the equation. Adding x to both sides of 2 x + 5 = − 10 − x gives 2 x + x + 5 = − 10 − x + x , which simplifies to 3 x + 5 = − 10 .
Justifying Step 2 Step 2: From 3 x + 5 = − 10 to 3 x = − 15 , we observe that 5 was subtracted from both sides of the equation. Subtracting 5 from both sides of 3 x + 5 = − 10 gives 3 x + 5 − 5 = − 10 − 5 , which simplifies to 3 x = − 15 .
Justifying Step 3 Step 3: From 3 x = − 15 to x = − 5 , we observe that both sides of the equation were divided by 3. Dividing both sides of 3 x = − 15 by 3 gives 3 3 x = 3 − 15 , which simplifies to x = − 5 .
Conclusion Therefore, the justifications for Marlena's steps are: Step 1: Add x to both sides of the equation. Step 2: Subtract 5 from both sides of the equation. Step 3: Divide both sides of the equation by 3.
Examples
Solving linear equations like this is a fundamental skill in algebra. It's used in many real-world situations, such as calculating the cost of items with discounts or taxes, determining distances and speeds, or even in more complex scenarios like financial planning and engineering calculations. For example, if you want to buy a shirt that costs $25 after a 20% discount and a $5 tax, you can set up an equation to find the original price of the shirt before the discount and tax.
