Question

1. 7a - 6 + 8a
2. -3d + 8d - 5d
3. 1.5g - 10 + 0.5g - 3
4. \\( \frac { 1 } { 2 } h + 2 h + \frac { 3 } { 2 } h - 1 \\)
5. write and simplify an expression that represents the perimeter of the rectangle shown.

7.5 12y

Explanation:

Step1: Combine like terms for \(7a - 6+8a\)

Combine \(7a\) and \(8a\): \((7a + 8a)-6=15a - 6\)

Step2: Combine like terms for \(-3d + 8d-5d\)

\((-3d + 8d-5d)=( - 3 + 8-5)d=0d = 0\)

Step3: Combine like terms for \(1.5g-10 + 0.5g-3\)

Combine \(1.5g\) and \(0.5g\), and \(-10\) and \(-3\): \((1.5g+0.5g)+(-10 - 3)=2g-13\)

Step4: Combine like terms for \(\frac{1}{2}h+2h+\frac{3}{2}h - 1\)

Convert \(2h=\frac{4}{2}h\). Then \((\frac{1}{2}h+\frac{4}{2}h+\frac{3}{2}h)-1=\frac{1 + 4+3}{2}h-1 = 4h-1\)

Step5: Find the perimeter of the rectangle

The formula for the perimeter of a rectangle is \(P = 2(l + w)\), where \(l = 12y\) and \(w = 7.5\)
\(P=2(12y + 7.5)=2\times12y+2\times7.5 = 24y+15\)

Answer:

1. \(15a - 6\)
2. \(0\)
3. \(2g-13\)
4. \(4h - 1\)
5. \(24y + 15\)