Question

work with a partner. use algebra tiles to model and solve the equation.
a. ( x - 3 = - 4 )
model the equation ( x - 3 = - 4 ). draw a sketch of your tiles.
to get the variable tile by itself, remove the __ tiles on the left side by adding __ tiles to each side.
how many zero pairs can you remove from each side? circle them.
the remaining tiles show the value of ( x ).
( x = )
b. ( z - 6 = 2 )
c. ( p - 7 = - 3 )
d. ( - 15 = t - 5 )

Explanation:

Step1: Solve \(x - 3=-4\)

Add \(3\) to both sides of the equation \(x-3 = - 4\). According to the addition property of equality, if \(a=b\), then \(a + c=b + c\).
$$x-3+3=-4 + 3$$

Step2: Simplify the equation

Simplify the left - hand side: \(x-3 + 3=x\). Simplify the right - hand side: \(-4+3=-1\).

Step3: Solve \(z - 6=2\)

Add \(6\) to both sides of the equation \(z - 6=2\).
$$z-6 + 6=2+6$$
Simplify to get \(z = 8\).

Step4: Solve \(p-7=-3\)

Add \(7\) to both sides of the equation \(p - 7=-3\).
$$p-7+7=-3 + 7$$
Simplify to get \(p = 4\).

Step5: Solve \(-15=t - 5\)

Add \(5\) to both sides of the equation \(-15=t - 5\).
$$-15 + 5=t-5+5$$
Simplify to get \(t=-10\).

Answer:

a. \(x=-1\)
b. \(z = 8\)
c. \(p = 4\)
d. \(t=-10\)