Equations with Variables on Both Sides! Please help!

x = 12

Step-by-step explanation:

-x + 8 = x - 16

add x to both sides

8 = 2x - 16

add 16 to both sides

24 = 2x

divide by 2 on both sides

x = 12

x = 12

Step-by-step explanation:

you can do any of the following as the first step:

a)  add 'x' to each side to get:  8 = 2x - 16

b)  subtract 'x' from each side to get:  -2x + 8 = -16

c) subtract 8 from each side to get:  -x = x -24

d) add 16 to each side to get:  -x + 24 = x

if we choose to solve the equation in (a) we will get:

8 = 2x - 16

8 + 16 = 2x - 16 + 16 which simplifies to:

24 = 2x

divide each side by 2 to get x = 12

solving any of the above 4 equation will give you x = 12

answer: (c) m∠qpo + (2x + 16)° = 180°

step-by-step explanation:

the opposite angles of a quadrilateral are supplementary.

so, ∠o + ∠q = 180°   and   ∠p + ∠r = 180°

since ∠r = 2x + 16°, we can use substitution as follows:

∠p + ∠r = 180°

∠p + (2x + 16)° = 180°

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true