1. To graph y=1/x, you can start by creating a table of values. Choose some x-values, and then calculate the corresponding y-values by substituting the x-values into the equation. Once you have a few points, plot them on a graph. Also, include the point (0,0) since x cannot be zero in the equation.
2. To find the x-intercepts, set y=0 in the equation and solve for x. These are the points where the graph intersects the x-axis. To find the y-intercept, set x=0 and solve for y. This is the point where the graph intersects the y-axis.
Checking your solutions:
9. (-4x-2)+7=-3(x+3)
Simplifying both sides:
-4x + 5 = -3x - 9
Combining like terms:
x = -14
10. -2[7x-7-6(x+1)]=2x+5
Simplifying both sides:
-14x + 14 + 12x + 12 = 2x + 5
Combining like terms:
-2x + 26 = 2x + 5
Combining like terms again:
4x = 21
Dividing by 4:
x = 21/4
13. (x+7)/4=2-(x-1)/6
Multiply both sides by the least common denominator, which is 12:
3(x+7) = 24 - 2(x-1)
Simplify both sides:
3x + 21 = 24 - 2x + 2
Combining like terms:
5x + 19 = 26
Combining like terms again:
5x = 7
Dividing by 5:
x = 7/5
16. y1 = (x+6)/3, y2 = (x+8)/6, y1 = y2
Setting the two equations equal to each other:
(x+6)/3 = (x+8)/6
To eliminate the fractions, multiply both sides by 6:
2(x+6) = x+8
Simplifying both sides:
2x + 12 = x + 8
Combining like terms:
x = -4
19. (x-8)/2x + 5 = (x+6)/x
Multiplying both sides by 2x to eliminate fractions:
(x-8) + 5(2x) = (x+6)(2x)
Expanding and simplifying:
x - 8 + 10x = 2x^2 + 12x
Combining like terms:
11x - 8 = 2x^2 + 12x
Rearranging and combining like terms again:
2x^2 + x - 8 = 0
This is a quadratic equation that can be factored or solved using the quadratic formula.
24. -2(x+7) + 52 = 4x - 6(x+3)
Simplifying both sides:
-2x - 14 + 52 = 4x - 6x - 18
Combining like terms:
-2x + 38 = -2x - 18
Adding 2x to both sides:
38 = -18
This is a contradiction, so the equation is inconsistent. There is no solution.
25. (3x+2)/4 + 2 = -7x/2
Multiplying through by 4 to eliminate fractions:
3x + 2 + 8 = -14x
Combining like terms:
3x + 10 = -14x
Adding 14x to both sides:
17x + 10 = 0
Subtracting 10 from both sides:
17x = -10
Dividing by 17:
x = -10/17
Please note that it's always a good idea to double-check your work and solutions to make sure they are correct.