Solve for x and graph the solution on the number line below.

See image

Step-by-step explanation:

"Solve for x" means get the x all by itself. So multiply by -2 on both sides of the inequality. When you multiply by a negative number like that ***!!!*** its VERY important that you reverse the inequality symbol in the math sentence.

x/-2 <= -2

(-2) x/-2 <= -2 (-2)

x >= 4

This sentence can now be graphed on a number line. It says 'all the numbers bigger than four or equal to four' See image for graph.

Since there is an equal to bar under the greater (less) than symbol. You use a closed dot (sometimes higher level math classes want you to use a square bracket instead [ The closed dot or square bracket means the four is included in the answer. The arrow goes to the right, because those are all the numbers bigger than four.

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12