Test: Linear Equations in one Variable - Grade 8 MCQ

After adding 7 to both sides of 3y - 7 = 16, we get 3y = 23. The next step is to divide both sides by 3, resulting in y = 23/3.

The equation x + (x + 2) = 36 is formed to represent the sum of two consecutive odd numbers. This equation reflects the relationship between the first and the second odd number.

To solve 3y = 9, divide both sides by 3, resulting in y = 3. This is a straightforward solution that showcases the basic principle of isolating the variable.

After dividing both sides of 2x = 10 by 2, we obtain x = 5. This is the solution that satisfies the equation, demonstrating the isolation of the variable.

By adding 10 to both sides of the equation 5z - 10 = 0, we find that 5z = 10. Dividing both sides by 5 gives z = 2, which is the root of the equation.

A linear equation in one variable is expressed in the form ax + b = 0, where 'a' and 'b' are constants, and 'a' cannot equal zero. This form signifies that the equation represents a straight line when graphed.

The first step in solving the word problem is to represent the unknown number as a variable, such as "Let the number be x." This allows us to form the equation 2x = x + 10 in the next step.

Consecutive even numbers can be represented as x, x + 2, x + 4, where x is an even integer. This shows the difference of 2 between each successive even number.

Consecutive multiples of 3 starting from x can be represented as x, x + 3, x + 6. This pattern maintains the consistent difference of 3 among the multiples.

A root of 4 means that when x is substituted with 4 in the equation, both sides of the equation are equal. This indicates that x = 4 satisfies the equation, confirming it as a valid solution.

To solve the equation 2x - 1 = 3, first add 1 to both sides, yielding 2x = 4. Then, dividing by 2 gives x = 2. This solution illustrates the step-by-step process of isolating the variable.

If we let x represent the age of the son and y represent the age of the man, the equation y = x + 24 correctly expresses that the man is 24 years older than his son. This relationship is crucial for solving age-related problems.

To isolate the variable in the equation 2x + 5 = 11, the first step is to subtract 5 from both sides, resulting in 2x = 6. This allows us to further solve for x.

The correct approach to solving word problems is to carefully identify the known and unknown quantities and then form an appropriate equation based on the relationships described. This structured method ensures a logical solution.

To solve 4x - 8 = 0, first add 8 to both sides to get 4x = 8, and then divide by 4, resulting in x = 2. This is the value that satisfies the equation.

To isolate x in the equation 2x - 3 = 7, the correct first step is to add 3 to both sides, resulting in 2x = 10. This prepares for the next step of dividing by 2 to find x.

The new perimeter after increasing each side by x cm would be calculated as 2[(8 + x) + (5 + x)], which simplifies to 26 + 4x. This reflects the increase in perimeter due to the adjustment in dimensions.

Subtracting a different number from both sides does not maintain the equality of the equation. In contrast, adding, multiplying, or dividing by the same non-zero number keeps the equation balanced.

When the original length of 8 cm is increased by 6.5 cm, the new length becomes 8 + 6.5 = 14.5 cm. This calculation reflects the adjustment made to the rectangle's dimensions.

A linear equation in one variable has exactly one solution, known as its root. This characteristic is fundamental to understanding linear equations and their graphical representation as straight lines.