Step by step

g i bisects ∠ d g h so that m ∠ d g i is x − 3 and m ∠ i g h is 2 x − 13 . gi→ bisects ∠dgh so that m ∠dgi is x-3 and m ∠igh is 2x -13.find the value of x.

x = 10

Step-by-step explanation:

Always draw a diagram if one is not given.

Since GI bisects ∠DGH, its two new angles that are formed (∠DGI and ∠IGH)are equal.

∠DGI = ∠IGH     Substitute the expressions for each angle

x - 3 = 2x - 13        Isolate x to solve

x - x - 3 = 2x - x - 13       Subtract x from both sides

-3 = x - 13        Simplified

-3 + 13 = x - 13 + 13       Add 13 to both sides

10 = x       Simplified, also the answer

x = 10       Variable on left side is standard

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

the answer is d

step-by-step explanation: