To solve the problem in the image, it involves comparing algebraic expressions represented by tiles. Each tile type (large, small, shaded, unshaded) represents different values, and your task is to simplify both sides (left and right) of the comparison mat to determine which is greater.

Let's break this down:

Key (from the image symbols):

• Large black square = $x$
• Small black square = $1$
• Large white square = $-x$
• Small white square = $-1$

Part (a):

• Left side:

  • Top section: $+1x, +1x, +1, -1, -1$ → Simplifies to $2x - 1$
  • Bottom section: $-1x, +1$ → Simplifies to $-x + 1$

  Combined: $(2x - 1) + (-x + 1) = x$

• Right side:

  • Top section: $+1x, +1$ → Simplifies to $x + 1$
  • Bottom section: $-1, -1$ → Simplifies to $-2$

  Combined: $(x + 1) + (-2) = x - 1$

So, for part (a):

• Left side = $x$
• Right side = $x - 1$

Clearly, the left side is greater because $x$ is greater than $x - 1$.

Part (b):

• Left side:

  • Top section: $+x, +1x, -1x, +1$ → Simplifies to $x + 1$
  • Bottom section: $-1x, -1$ → Simplifies to $-x - 1$

  Combined: $(x + 1) + (-x - 1) = 0$

• Right side:

  • Top section: $+1x, -1$ → Simplifies to $x - 1$
  • Bottom section: $-1x$ → Simplifies to $-x$

  Combined: $(x - 1) + (-x) = -1$

So, for part (b):

• Left side = $0$
• Right side = $-1$

Clearly, the left side is greater because $0$ is greater than $-1$.

Would you like more details or further clarification?

5 Related Questions:

1. How do you simplify algebraic expressions using tiles?
2. What is the process for solving inequalities?
3. How do you represent negative numbers with algebra tiles?
4. How can we compare expressions involving variables and constants?
5. What techniques are useful when solving problems with unknowns on both sides?

Tip:

Always combine like terms when comparing two sides of an equation or inequality. Simplifying each side helps identify which side is greater easily.