Question

5 label the arrows to describe each move. 3(x + 1) = 5+2 3(x + 1) = 7 3x + 3 = 7 3x = 4 x = 4/3

Explanation:

Step1: Simplify right - hand side

The first move from \(3(x + 1)=5 + 2\) to \(3(x + 1)=7\) is simplifying the arithmetic on the right - hand side. We calculate \(5+2\) which equals \(7\). So this step is "Simplify \(5 + 2\) to \(7\)".

Step2: Distribute the 3

The move from \(3(x + 1)=7\) to \(3x+3 = 7\) is using the distributive property of multiplication over addition. The distributive property states that \(a(b + c)=ab+ac\). Here, \(a = 3\), \(b=x\) and \(c = 1\), so \(3(x + 1)=3\times x+3\times1=3x + 3\). So this step is "Distribute \(3\) over \((x + 1)\)".

Step3: Subtract 3 from both sides

The move from \(3x + 3=7\) to \(3x=4\) is subtracting \(3\) from both sides of the equation. If we have \(3x+3 = 7\), then by the subtraction property of equality (if \(a=b\), then \(a - c=b - c\)), we subtract \(3\) from both sides: \((3x + 3)-3=7 - 3\), which simplifies to \(3x=4\). So this step is "Subtract \(3\) from both sides".

Step4: Divide both sides by 3

The move from \(3x = 4\) to \(x=\frac{4}{3}\) is dividing both sides of the equation by \(3\). By the division property of equality (if \(a=b\) and \(c
eq0\), then \(\frac{a}{c}=\frac{b}{c}\)), we divide both sides of \(3x = 4\) by \(3\): \(\frac{3x}{3}=\frac{4}{3}\), which simplifies to \(x=\frac{4}{3}\). So this step is "Divide both sides by \(3\)".

Answer:

• From \(3(x + 1)=5 + 2\) to \(3(x + 1)=7\): Simplify \(5 + 2\) to \(7\)
• From \(3(x + 1)=7\) to \(3x+3 = 7\): Distribute \(3\) over \((x + 1)\)
• From \(3x + 3=7\) to \(3x=4\): Subtract \(3\) from both sides
• From \(3x = 4\) to \(x=\frac{4}{3}\): Divide both sides by \(3\)