Question

8.4x + 6.3x + 12.6 as an equivalent expression for 4.2(2x + 1.5x + 3). she said that her equivalent expression is simplified. do you agree? explain.

Explanation:

Step1: Simplify the left - hand side expression

First, we simplify the expression \(8.4x + 6.3x+12.6\). We can combine like terms (the terms with \(x\)). Using the rule of combining like terms \(ax + bx=(a + b)x\), where \(a = 8.4\) and \(b = 6.3\), we have:
\(8.4x+6.3x=(8.4 + 6.3)x=14.7x\)
So the left - hand side expression simplifies to \(14.7x + 12.6\).

Step2: Simplify the right - hand side expression

Now, we simplify the expression \(4.2(2x + 1.5x+3)\). First, combine the like terms inside the parentheses. For the terms with \(x\) inside the parentheses: \(2x+1.5x=(2 + 1.5)x = 3.5x\).
So the expression inside the parentheses becomes \(3.5x + 3\). Then we use the distributive property \(a(b + c)=ab+ac\), where \(a = 4.2\), \(b = 3.5x\) and \(c = 3\).
\(4.2\times3.5x+4.2\times3\)
Calculate \(4.2\times3.5\): \(4.2\times3.5=(4 + 0.2)\times3.5=4\times3.5+0.2\times3.5 = 14+0.7 = 14.7\)
Calculate \(4.2\times3 = 12.6\)
So the right - hand side expression simplifies to \(14.7x+12.6\).

Answer:

Since both the left - hand side expression \(8.4x + 6.3x+12.6\) and the right - hand side expression \(4.2(2x + 1.5x + 3)\) simplify to \(14.7x+12.6\), we agree that her equivalent expression is simplified correctly.