Question

using the key at the right, type the equation and the solution for each of the models below. key: green rectangle = x, red rectangle = -x, yellow square = 1, red square = -1 (models labeled a, b, c, d with balance scales and spaces for equation and solution)

Explanation:

Part A

Step1: Count left - hand side (LHS) and right - hand side (RHS)

• LHS: 1 green bar ($x$) and 4 yellow squares (each = 1), so LHS is $x + 4$.
• RHS: 11 yellow squares, so RHS is $11$.
• Equation: $x + 4=11$.

Step2: Solve for $x$

Subtract 4 from both sides: $x=11 - 4$.
$x = 7$.

Step1: Count LHS and RHS

• LHS: 1 green bar ($x$) and 5 red squares (each = - 1), so LHS is $x-5$.
• RHS: 9 yellow squares, so RHS is $9$.
• Equation: $x - 5=9$.

Step2: Solve for $x$

Add 5 to both sides: $x=9 + 5$.
$x = 14$.

Step1: Count LHS and RHS

• LHS: 1 green bar ($x$) and 7 red squares (each = - 1), so LHS is $x-7$.
• RHS: 7 yellow squares, so RHS is $7$.
• Equation: $x - 7=7$.

Step2: Solve for $x$

Add 7 to both sides: $x=7 + 7$.
$x = 14$.

Answer:

Equation: $x + 4=11$; Solution: $x = 7$

Part B