QuestionTranslate the following sentence to an equation. Then solve the equation.
Twenty-six less a number is equal to the product of 2 and the sum of the number and 7 . Find the number.
The equation is
(Type an equation using as the variable. Do not simplify.)
The number is .
(Simplify your answer.)
Studdy Solution
STEP 1
What is this asking? We need to translate a word problem into a mathematical equation and then solve for the unknown number. Watch out! Be careful with the order of operations and make sure to correctly interpret "less than" and "product of."
STEP 2
1. Translate the sentence into an equation.
2. Solve the equation for .
STEP 3
This translates to subtracted from an unknown number, which we'll call .
So, we have .
STEP 4
This simply means we use an equals sign: .
STEP 5
The "sum of the number and 7" is .
The "product of 2 and" this sum means we multiply the sum by : .
STEP 6
Putting it all together, our equation is:
STEP 7
Distribute the on the right side of the equation:
STEP 8
Subtract from both sides to get all the terms on one side:
STEP 9
Subtract from both sides to isolate :
STEP 10
So, .
STEP 11
The equation is . The number is .
Was this helpful?