QuestionFind the number of solutions for the equation: $5x + 2 - 2(x - 1) = 3x + 4$ .

Studdy Solution

STEP 1

Assumptions1. The equation is a linear equation in one variable (x). . The equation is in the form of $ax + b = cx + d$ .

STEP 2

First, we need to simplify the equation. We can do this by distributing the multiplication over the parentheses on the left side of the equation.
$5x +2 -2(x -1) =5x +2 -2x +2$

STEP 3

Now, we simplify the left side of the equation by combining like terms.
$5x -2x +2 +2 =3x +$

STEP 4

This simplifies to $3x +4 =3x +4$

STEP 5

Now, we can subtract $3x$ from both sides of the equation to isolate $x$ .
$3x -3x +4 =3x -3x +4$

STEP 6

This simplifies to $4 =4$

STEP 7

Since the left side of the equation is equal to the right side of the equation for all values of $x$ , we can say that there are infinitely many solutions to this equation.
So, the solution to the equation is There are infinitely many solutions.

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QuestionFind the number of solutions for the equation: $5x + 2 - 2(x - 1) = 3x + 4$ .

Studdy Solution

STEP 1

Assumptions1. The equation is a linear equation in one variable (x). . The equation is in the form of $ax + b = cx + d$ .

STEP 2

First, we need to simplify the equation. We can do this by distributing the multiplication over the parentheses on the left side of the equation.
$5x +2 -2(x -1) =5x +2 -2x +2$

STEP 3

Now, we simplify the left side of the equation by combining like terms.
$5x -2x +2 +2 =3x +$

STEP 4

This simplifies to $3x +4 =3x +4$

STEP 5

Now, we can subtract $3x$ from both sides of the equation to isolate $x$ .
$3x -3x +4 =3x -3x +4$

STEP 6

This simplifies to $4 =4$

STEP 7

Since the left side of the equation is equal to the right side of the equation for all values of $x$ , we can say that there are infinitely many solutions to this equation.
So, the solution to the equation is There are infinitely many solutions.

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QuestionFind the number of solutions for the equation: 5x+2−2(x−1)=3x+45x + 2 - 2(x - 1) = 3x + 45x+2−2(x−1)=3x+4.

Studdy Solution

STEP 1

Assumptions1. The equation is a linear equation in one variable (x). . The equation is in the form of ax+b=cx+dax + b = cx + dax+b=cx+d.

STEP 2

First, we need to simplify the equation. We can do this by distributing the multiplication over the parentheses on the left side of the equation.5x+2−2(x−1)=5x+2−2x+25x +2 -2(x -1) =5x +2 -2x +25x+2−2(x−1)=5x+2−2x+2

STEP 3

Now, we simplify the left side of the equation by combining like terms.5x−2x+2+2=3x+5x -2x +2 +2 =3x +5x−2x+2+2=3x+

STEP 4

This simplifies to3x+4=3x+43x +4 =3x +43x+4=3x+4

STEP 5

Now, we can subtract 3x3x3x from both sides of the equation to isolate xxx.3x−3x+4=3x−3x+43x -3x +4 =3x -3x +43x−3x+4=3x−3x+4

STEP 6

This simplifies to4=44 =44=4

STEP 7

Since the left side of the equation is equal to the right side of the equation for all values of xxx, we can say that there are infinitely many solutions to this equation.So, the solution to the equation is There are infinitely many solutions.

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QuestionFind the number of solutions for the equation: $5x + 2 - 2(x - 1) = 3x + 4$ .

Assumptions1. The equation is a linear equation in one variable (x). . The equation is in the form of $ax + b = cx + d$ .

First, we need to simplify the equation. We can do this by distributing the multiplication over the parentheses on the left side of the equation.
$5x +2 -2(x -1) =5x +2 -2x +2$

Now, we simplify the left side of the equation by combining like terms.
$5x -2x +2 +2 =3x +$

This simplifies to $3x +4 =3x +4$

Now, we can subtract $3x$ from both sides of the equation to isolate $x$ .
$3x -3x +4 =3x -3x +4$

This simplifies to $4 =4$

Since the left side of the equation is equal to the right side of the equation for all values of $x$ , we can say that there are infinitely many solutions to this equation.
So, the solution to the equation is There are infinitely many solutions.