Question

solve the equation \\(\frac{x + 7}{2} = 15\\) for \\(x\\). show your work by filling in the boxes below with the appropriate equations and actions (in words) to describe what you did in that step of the process of solving the equation. - drag the initial equation to column 1, row 1 of the grid: \\(\frac{x + 7}{2} = 15\\). note: the
esulting equation after action\ for row 1 will be used again as the \starting equation on this step\ for row 2. step 1 starting equation on this step action (in words) resulting equation after action step 2 equations: \\(x = 0.5\\), \\(x = 4\\), \\(x = 11\\), \\(x = 14.5\\), \\(x = 16\\), \\(x = 23\\), \\(x = 33\\), \\(x = 37\\), \\(x = 44\\), \\(x + 7 = 7.5\\), \\(x + 7 = 30\\), \\(\frac{x}{2} = 8\\), \\(\frac{x}{2} = 22\\), \\(\frac{x + 7}{2} = 15\\) action (in words): add 7 to both sides of the equation. divide both sides of the equation by 2. multiply both sides of the equation by 2. subtract 7 from both sides of the equation.

Explanation:

Step 1:

Step1: Multiply both sides by 2

To eliminate the denominator, we multiply both sides of the equation $\frac{x + 7}{2}=15$ by 2. Using the multiplication property of equality (if $a = b$, then $a\times c=b\times c$), we get $2\times\frac{x + 7}{2}=15\times2$, which simplifies to $x + 7 = 30$.

Step2: Subtract 7 from both sides

To isolate $x$, we subtract 7 from both sides of the equation $x + 7 = 30$. Using the subtraction property of equality (if $a = b$, then $a - c=b - c$), we get $x+7 - 7=30 - 7$, which simplifies to $x = 23$.

Step 1 Table Entry:

• Starting Equation on This Step: $\boldsymbol{\frac{x + 7}{2}=15}$
• Action (in Words): Multiply both sides of the equation by 2.
• Resulting Equation After Action: $\boldsymbol{x + 7 = 30}$

Step 2 Table Entry:

• Starting Equation on This Step: $\boldsymbol{x + 7 = 30}$
• Action (in Words): Subtract 7 from both sides of the equation.
• Resulting Equation After Action: $\boldsymbol{x = 23}$

Answer:

Step 1:

• Starting Equation on This Step: $\frac{x + 7}{2}=15$
• Action (in Words): Multiply both sides of the equation by 2.
• Resulting Equation After Action: $x + 7 = 30$

Step 2:

• Starting Equation on This Step: $x + 7 = 30$
• Action (in Words): Subtract 7 from both sides of the equation.
• Resulting Equation After Action: $x = 23$