The equation has infinite amount of solutions.
2(4x+7)-7=
Finsish the equation so that the equation that has zero solutions
5(5x+3)-2=
Find the value of x that makes the following have exactly 1 solution
-4(2x+10)=-3x+5
To find the solution for each equation:
1. 2(4x+7)-7=
Distribute the 2: 8x + 14 - 7 =
Combine like terms: 8x + 7 = 0
Isolate 8x: 8x = -7
Divide by 8: x = -7/8
Therefore, the equation has a single solution: x = -7/8.
2. 5(5x+3)-2=
Distribute the 5: 25x + 15 - 2 =
Combine like terms: 25x + 13 = 0
Isolate 25x: 25x = -13
Divide by 25: x = -13/25
Therefore, the equation has a single solution: x = -13/25.
3. -4(2x+10)=-3x+5
Distribute the -4: -8x - 40 = -3x + 5
Combine like terms: -8x + 3x = 5 + 40
Simplify: -5x = 45
Divide by -5: x = 45/-5
Simplify further: x = -9
Therefore, the equation has a single solution: x = -9.
To determine the solutions for each equation, let's solve them step by step.
1) For the equation 2(4x+7) - 7 = 0:
Start by distributing the 2:
8x + 14 - 7 = 0
Simplify:
8x + 7 = 0
Move 7 to the other side by subtracting 7 from both sides:
8x = -7
Divide both sides by 8:
x = -7/8
Therefore, the equation has a single solution with x = -7/8.
2) For the equation 5(5x+3) - 2 = 0:
Start by distributing the 5:
25x + 15 - 2 = 0
Simplify:
25x + 13 = 0
Move 13 to the other side by subtracting 13 from both sides:
25x = -13
Divide both sides by 25:
x = -13/25
Therefore, the equation has a single solution with x = -13/25.
3) For the equation -4(2x+10) = -3x + 5:
Start by distributing the -4:
-8x - 40 = -3x + 5
Simplify:
-8x + 40 = -3x + 5
Move -3x to the other side by adding 3x to both sides:
-5x + 40 = 5
Move 40 to the other side by subtracting 40 from both sides:
-5x = -35
Divide both sides by -5:
x = 7
Therefore, the equation has a single solution with x = 7.
To determine the number of solutions to an equation, we need to solve the equation and analyze the resulting solution(s).
Let's start with the equation 2(4x+7)-7=0:
1. Distribute the 2 to both terms inside the parentheses:
8x + 14 - 7 = 0
2. Combine like terms:
8x + 7 = 0
3. To isolate x, subtract 7 from both sides:
8x = -7
4. Finally, divide both sides by 8 to solve for x:
x = -7/8
Now let's move on to the equation 5(5x+3)-2=0. We want to adjust this equation so that it has no solutions:
1. Distribute the 5 to both terms inside the parentheses:
25x + 15 - 2 = 0
2. Combine like terms:
25x + 13 = 0
3. To eliminate the 13 on the right side, we cannot simply add or subtract a number.
Since the left side contains a multiple of x, we cannot make it be equal to zero.
Therefore, we cannot make this equation have zero solutions.
Finally, let's find the value of x that makes -4(2x+10)=-3x+5 have exactly one solution:
1. Distribute the -4 to both terms inside the parentheses:
-8x - 40 = -3x + 5
2. Move all terms with x to one side and constant terms to the other side:
-8x + 3x = 5 + 40
3. Combine like terms:
-5x = 45
4. To solve for x, divide both sides by -5:
x = -45/5
Simplifying,
x = -9
Hence, the value of x that makes the equation -4(2x+10)=-3x+5 have exactly one solution is x = -9.