Question

drag each tile to the correct box.
arrange the equations in order from least to greatest based on their solution.
equation a: $5(x - 6) + 3x = \frac{3}{4}(2x - 8)$
equation b: $2.7(5.1x + 4.9) = 3.2x + 28.9$
equation c: $5(11x - 18) = 3(2x + 7)$
equation a equation b equation c
$\square$ < $\square$ < $\square$

Explanation:

Step1: Solve Equation A

First, expand both sides:
Left side: \(5(x - 6)+3x = 5x - 30 + 3x = 8x - 30\)
Right side: \(\frac{3}{4}(2x - 8)=\frac{3}{4}\times2x-\frac{3}{4}\times8=\frac{3}{2}x - 6\)
Now, set up the equation: \(8x - 30=\frac{3}{2}x - 6\)
Subtract \(\frac{3}{2}x\) from both sides: \(8x-\frac{3}{2}x - 30=- 6\)
\(\frac{13}{2}x - 30=- 6\)
Add 30 to both sides: \(\frac{13}{2}x=24\)
Multiply both sides by \(\frac{2}{13}\): \(x = \frac{48}{13}\approx3.69\)

Step2: Solve Equation B

Expand the left side: \(2.7(5.1x + 4.9)=2.7\times5.1x+2.7\times4.9 = 13.77x+13.23\)
Set up the equation: \(13.77x + 13.23=3.2x + 28.9\)
Subtract \(3.2x\) from both sides: \(13.77x-3.2x + 13.23=28.9\)
\(10.57x + 13.23=28.9\)
Subtract 13.23 from both sides: \(10.57x=28.9 - 13.23 = 15.67\)
Divide both sides by 10.57: \(x=\frac{15.67}{10.57}\approx1.48\)

Step3: Solve Equation C

Expand both sides:
Left side: \(5(11x - 18)=55x - 90\)
Right side: \(3(2x + 7)=6x + 21\)
Set up the equation: \(55x - 90=6x + 21\)
Subtract \(6x\) from both sides: \(55x-6x - 90=21\)
\(49x - 90=21\)
Add 90 to both sides: \(49x=111\)
Divide both sides by 49: \(x=\frac{111}{49}\approx2.27\)

Step4: Compare the solutions

We have \(x_A\approx3.69\), \(x_B\approx1.48\), \(x_C\approx2.27\)
So, from least to greatest: \(x_B

Answer:

Equation B < Equation C < Equation A