Find the length of the variable w

w = 3

Step-by-step explanation:

Δ BDE and Δ BAC are similar, then the ratios of corresponding sides are equal, that is

= , substitute values

= ( cross- multiply )

5w = 3(w + 2) ← distribute

5w = 3w + 6 ( subtract 3w from both sides )

2w = 6 ( divide both sides by 2 )

w = 3

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step-by-step explanation:

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