Linear Equations - Examples, Exercises and Solutions

To solve the equation$5x \cdot 3 = 45$, follow these steps:

1. First, identify the operation needed to solve for$x$. In this case, we have a multiplication equation.

2. Therefore, we divide both sides of the equation by 15 (since $5 \times 3 = 15$) to isolate $x$:

$x = \frac{45}{15}$

3. Calculate $x$:

$x = 3$

To solve$2 + x - 5 = 4 - 3$, we first simplify both sides:

Left side:
$2 - 5 + x = -3 + x$

Right side:
$4 - 3 = 1$

Now the equation is $-3 + x = 1$.

Add 3 to both sides:
$x = 1 + 3$

So,$x = 4$.

First, simplify the right side of the equation:
$10 - 6 = 4$
Hence, the equation becomes $3 - x = 4$.
Subtract 3 from both sides to isolate $x$:
$3 - x - 3 = 4 - 3$
This simplifies to:
$-x=1$
Divide by -1 to solve for$x$:
$x=-1$
Therefore, the solution is $x = 1$.

To solve $3 + x + 1 = 6 - 2$, we first simplify both sides:

Left side:
$3 + 1 + x = 4 + x$

Right side:
$6 - 2 = 4$

Now the equation is $4 + x = 4$.

Subtract 4 from both sides:
$x = 4 - 4$

So, $x = 0$.

First, simplify both sides of the equation:

Left side: $3 + x - 2 = 1 + x$

Right side: $7 - 3 = 4$

So the equation becomes:

$1 + x = 4$

Next, isolate $x$ by subtracting 1 from both sides:

$1 + x - 1 = 4 - 1$

This simplifies to:

$x = 3$

First, simplify the right side of the equation:
$12 - 4 = 8$
Hence, the equation becomes $5 - x = 8$.
Subtract 5 from both sides to isolate $x$:
$5 - x - 5 = 8 - 5$
This simplifies to:
$-x=3$
Divide by -1 to solve for $x$:
$x=-3$
Therefore, the solution is $x=-3$.

To solve $5 + x - 3 = 2 + 1$, we first simplify both sides:

Left side:
$5 - 3 + x = 2 + x$$$

Right side:
$2 + 1 = 3$

Now the equation is $2 + x = 3$.

Subtract 2 from both sides:
$x = 3 - 2$

So, $x = 1$.

To solve the equation $6 - x = 10 - 2$, follow these steps:

1. First, simplify both sides of the equation:

2. On the right side, calculate $10 - 2 = 8$.

3. The equation simplifies to $6 - x = 8$.

4. To isolate x, subtract 6 from both sides:

5. $6 - x - 6 = 8 - 6$

6. This simplifies to $-x = 2$.

7. Multiply both sides by -1 to solve for x:

8. $x = -2 \times -1 = 2$.

9. Since the problem requires only manipulation by transferring terms, the initial approach to the equation setup should lead to x = 4 as the solution before re-evaluation.

Therefore, the correct solution to the equation is $x=2$.

First, simplify the right side of the equation:
$15 - 5 = 10$
Hence, the equation becomes $7 - x = 10$.
Subtract 7 from both sides to isolate $x$:
$7 - x - 7 = 10 - 7$
This simplifies to:
$-x=3$
Divide by -1 to solve for$x$:
$x=-3$
Therefore, the solution is $x=-3$.

First, simplify the right side of the equation:
$11 - 3 = 8$
Hence, the equation becomes $8 - x = 8$.
Subtract 8 from both sides to isolate $x$:
$8 - x - 8 = 8 - 8$
This simplifies to:
$-x=0$
Divide by -1 to solve for $x$:
$x = 0$
Therefore, the solution is $x = 0$.

First, simplify the right side of the equation:
$16 - 7 = 9$
Hence, the equation becomes $9 - x = 9$.
Since both sides are equal, $x$ must be $0$.
Therefore, the solution is $x = 0$.

First, simplify both sides of the equation:

Left side: $x - 3 + 5 = x + 2$

Right side: $8 - 2 = 6$

Now the equation is: $x + 2 = 6$

Subtract 2 from both sides to isolate $x$:

$x + 2 - 2 = 6 - 2$

Simplifying gives:

$x = 4$

First, simplify both sides of the equation:

Left side: $x + 4 - 2 = x + 2$

Right side: $6 + 1 = 7$

Now the equation is: $x + 2 = 7$

Subtract 2 from both sides to isolate$x$:

$x + 2 - 2 = 7 - 2$

Simplifying gives:

$x = 5$

To solve the equation $6x \cdot 2 = 24$, follow these steps:

1. First, identify the operation involved. In this case, it is multiplication.

2. Divide both sides of the equation by 12 (since $6 \times 2 = 12$) to isolate $x$:

$x = \frac{24}{12}$

3. Calculate $x$:

$x = 2$

To solve the exercise, we first rewrite the entire division as a fraction:

$\frac{20}{4x}=5$

Actually, we didn't have to do this step, but it's more convenient for the rest of the process.

To get rid of the fraction, we multiply both sides of the equation by the denominator, 4X.

20=5*4X

20=20X

Now we can reduce both sides of the equation by 20 and we will arrive at the result of:

X=1