Question

1. mnop is a parallelogram. find the value of x. 5x - 8 = 4x = x = (there is a parallelogram mnop with diagonals intersecting at q. the length from m to q is 3x, from n to q is (5x - 8), and from p to q is (x + 24))

Explanation:

Step1: Recall parallelogram diagonal property

In a parallelogram, the diagonals bisect each other. So, \(5x - 8=x + 24\) (since \(NM\) and \(OP\) are equal as opposite sides, and the segments from the bisected diagonals relate to the sides? Wait, actually, in parallelogram \(MNOP\), \(NQ = QP\) and \(MQ = QO\), but also opposite sides are equal. Wait, the sides \(MN\) and \(OP\) are equal? Wait, the expressions are \(5x - 8\) (for \(MN\)) and \(x + 24\) (for \(OP\)), and \(3x\) for \(MQ\) or something? Wait, no, in a parallelogram, opposite sides are equal. So \(MN = OP\). So set \(5x - 8=x + 24\).

Step2: Solve for x from \(5x - 8=x + 24\)

Subtract \(x\) from both sides: \(5x - x- 8=x - x+ 24\) → \(4x - 8 = 24\)
Add 8 to both sides: \(4x - 8+ 8=24 + 8\) → \(4x=32\)
Divide both sides by 4: \(x=\frac{32}{4}=8\)

Wait, but let's check the steps. First, \(5x - 8=x + 24\) (because \(MN = OP\) in parallelogram). Then:

First blank: \(x + 24\) (since \(5x - 8=x + 24\))
Second blank: 32 (from \(4x = 32\))
Third blank: 8 (from \(x = 8\))

Wait, let's re - do:

1. In parallelogram \(MNOP\), opposite sides are equal. So \(MN = OP\). So \(5x - 8=x + 24\). So the first blank is \(x + 24\).

1. Then, from \(5x - 8=x + 24\), subtract \(x\) from both sides: \(4x-8 = 24\), then add 8: \(4x=24 + 8=32\). So second blank is 32.

1. Then, \(x=\frac{32}{4}=8\). So third blank is 8.

Answer:

First blank: \(x + 24\)
Second blank: \(32\)
Third blank: \(8\)