To find the value of x, we need to isolate x on one side of the equation.
Given: x - 5 = 2
To isolate x, we can add 5 to both sides of the equation:
x - 5 + 5 = 2 + 5
Simplifying, we have:
x = 7
Therefore, the value of x is 7.
If x−5=2 , then what is the value of x ?(1 point)
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3 answers
Which of the following pairs of equations has exactly the same solution?(1 point)
Responses
−3/4x=5/2 and 5/2x=−3/4
negative Start Fraction 3 over 4 End Fraction x equals Start Fraction 5 over 2 End Fraction and Start Fraction 5 over 2 End Fraction x equals negative Start Fraction 3 over 4 End Fraction
3/8x=1 and 1/3x=1/8
Start Fraction 3 over 8 End Fraction x equals 1 and Start Fraction 1 over 3 End Fraction x equals Start Fraction 1 over 8 End Fraction
x/3.2=1.8 and 1.8x=3.2
Start Fraction x over 3.2 End Fraction equals 1.8 and 1.8x equals 3.2
−3.2x=0.64 and x/4=−0.05
Responses
−3/4x=5/2 and 5/2x=−3/4
negative Start Fraction 3 over 4 End Fraction x equals Start Fraction 5 over 2 End Fraction and Start Fraction 5 over 2 End Fraction x equals negative Start Fraction 3 over 4 End Fraction
3/8x=1 and 1/3x=1/8
Start Fraction 3 over 8 End Fraction x equals 1 and Start Fraction 1 over 3 End Fraction x equals Start Fraction 1 over 8 End Fraction
x/3.2=1.8 and 1.8x=3.2
Start Fraction x over 3.2 End Fraction equals 1.8 and 1.8x equals 3.2
−3.2x=0.64 and x/4=−0.05
To determine which pairs of equations have exactly the same solution, we need to solve each pair of equations and compare the value of x in each case.
1) −3/4x=5/2 and 5/2x=−3/4
To solve the first equation, we can multiply both sides by -4/3:
(-4/3)(-3/4)x = (5/2)(-4/3)
x = -10/6
x = -5/3
To solve the second equation, we can multiply both sides by 2/5:
(2/5)(5/2)x = (-3/4)(2/5)
x = -6/20
x = -3/10
The values of x in the two equations are different, so this pair of equations does not have the same solution.
2) 3/8x=1 and 1/3x=1/8
To solve the first equation, we can multiply both sides by 8/3:
(8/3)(3/8)x = (1)(8/3)
x = 8/3
To solve the second equation, we can multiply both sides by 8/3:
(8/3)(1/3)x = (1/8)(8/3)
x = 8/9
The values of x in the two equations are different, so this pair of equations does not have the same solution.
3) x/3.2=1.8 and 1.8x=3.2
To solve the first equation, we can multiply both sides by 3.2:
(3.2)(x/3.2) = (1.8)(3.2)
x = 5.76
To solve the second equation, we can divide both sides by 1.8:
(1.8x)/1.8 = 3.2/1.8
x = 1.77777777...
The values of x in the two equations are approximately equal, but not exactly the same due to rounding, so this pair of equations does not have exactly the same solution.
4) −3.2x=0.64 and x/4=−0.05
To solve the first equation, we can divide both sides by -3.2:
(-3.2x)/-3.2 = (0.64)/-3.2
x = -0.2
To solve the second equation, we can multiply both sides by 4:
(4)(x/4) = (-0.05)(4)
x = -0.2
The values of x in the two equations are the same, -0.2, so this pair of equations has exactly the same solution.
Therefore, the correct answer is:
−3.2x=0.64 and x/4=−0.05.
1) −3/4x=5/2 and 5/2x=−3/4
To solve the first equation, we can multiply both sides by -4/3:
(-4/3)(-3/4)x = (5/2)(-4/3)
x = -10/6
x = -5/3
To solve the second equation, we can multiply both sides by 2/5:
(2/5)(5/2)x = (-3/4)(2/5)
x = -6/20
x = -3/10
The values of x in the two equations are different, so this pair of equations does not have the same solution.
2) 3/8x=1 and 1/3x=1/8
To solve the first equation, we can multiply both sides by 8/3:
(8/3)(3/8)x = (1)(8/3)
x = 8/3
To solve the second equation, we can multiply both sides by 8/3:
(8/3)(1/3)x = (1/8)(8/3)
x = 8/9
The values of x in the two equations are different, so this pair of equations does not have the same solution.
3) x/3.2=1.8 and 1.8x=3.2
To solve the first equation, we can multiply both sides by 3.2:
(3.2)(x/3.2) = (1.8)(3.2)
x = 5.76
To solve the second equation, we can divide both sides by 1.8:
(1.8x)/1.8 = 3.2/1.8
x = 1.77777777...
The values of x in the two equations are approximately equal, but not exactly the same due to rounding, so this pair of equations does not have exactly the same solution.
4) −3.2x=0.64 and x/4=−0.05
To solve the first equation, we can divide both sides by -3.2:
(-3.2x)/-3.2 = (0.64)/-3.2
x = -0.2
To solve the second equation, we can multiply both sides by 4:
(4)(x/4) = (-0.05)(4)
x = -0.2
The values of x in the two equations are the same, -0.2, so this pair of equations has exactly the same solution.
Therefore, the correct answer is:
−3.2x=0.64 and x/4=−0.05.
1 answer