Question

what equation does this set of algebra tiles represent? combine like terms on each side of the equation. for example, write 3 instead of 1 + 1 + 1.

Explanation:

Step1: Analyze left - hand side (LHS)

The left - hand side has two \(-x\) tiles. So the expression for LHS is \(-x+(-x)\), which simplifies to \(-2x\) (because when we add two like terms \(-x\) and \(-x\), we add their coefficients: \(- 1+(-1)=-2\) and the variable part remains \(x\)).

Step2: Analyze right - hand side (RHS)

The right - hand side has ten \(-1\) tiles. Let's count: there are 3 rows of 3 \(-1\) tiles (that's \(3\times3 = 9\)) and one additional \(-1\) tile. So in total, \(9 + 1=10\) \(-1\) tiles. So the expression for RHS is \(-1+(-1)+\cdots+(-1)\) (10 times), which is \(-10\).

Step3: Form the equation

Now that we have the simplified LHS and RHS, the equation is formed by setting LHS equal to RHS. So the equation is \(-2x=-10\).

Answer:

\(-2x = - 10\)