A circle is a figure in which each point around its perimeter is an equal distance from the center. The radius of a circle is the distance between the center and any point along its perimeter. A chord is a line segment that connects any two points along its perimeter. The diameter of a circle is the length of a chord that passes through the center of the circle and equals twice the circle's radius (2r).

To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the equal sign and the answer on the other.

-2x + 7 = -1 - 4x
-2x = -1 - 4x - 7
-2x + 4x = -1 - 7
2x = -8
x = \( \frac{-8}{2} \)
x = -4

Angles around a line add up to 180°. Angles around a point add up to 360°. When two lines intersect, adjacent angles are supplementary (they add up to 180°) and angles across from either other are vertical (they're equal).

A cylinder is a solid figure with straight parallel sides and a circular or oval cross section with a radius (r) and a height (h). The volume of a cylinder is π r²h and the surface area is 2(π r²) + 2π rh.

You need to find the value of a so solve the first equation in terms of x:

7a + x = -7
x = -7 - 7a

then substitute the result (-7 - 7a) into the second equation:

3a - 5(-7 - 7a) = 8
3a + (-5 x -7) + (-5 x -7a) = 8
3a + 35 + 35a = 8
3a + 35a = 8 - 35
38a = -27
a = \( \frac{-27}{38} \)
a = -\(\frac{27}{38}\)