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Chapter 6: Problem 53

Simplify each algebraic expression. \(7(3 y-5)+2(4 y+3)\)

Short Answer

Expert verified
The final simplified algebraic expression is \(29y - 29\)

Step by step solution

01

Distribute Multiplication Inside the Parentheses

By the property of distribution, distribute \(7\) within the first parentheses to get \(21y - 35\). Similarly, distribute \(2\) within the second parentheses to get \(8y + 6\). Then the expression becomes: \(21y - 35 + 8y + 6\)
02

Combine like terms

Once the multiplication has been distributed, group the 'y' terms together and the constants together. This gives: \(21y + 8y - 35 + 6\)
03

Simplify the expression

By simple arithmetic, \(21y + 8y\) equals \(29y\) and \(-35 + 6\) equals \(-29\). So, the simplified algebraic expression is \(29y - 29\)

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Most popular questions from this chapter

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I began the solution of \(5-3(x+2)>10 x\) by simplifying the left side, obtaining \(2 x+4>10 x\).

Solve the equations using the quadratic formula. \(x^{2}+5 x+3=0\)

Factor the trinomials , or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(6 x^{2}-11 x+4\)

Solve the quadratic equations in Exercises \(37-52\) by factoring. \(x^{2}+8 x+15=0\)

Factor the trinomials , or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(x^{2}-9 x-36\)
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