Questions & Answers

Question

Answers

Answer

Verified

92.1k+ views

The given equation is \[16\left( {3x - 5} \right) - 10\left( {4x - 8} \right) = 40\].

First, we will multiply the numbers with the terms inside the brackets using the distributive property of multiplication. Therefore, we get

\[ \Rightarrow 16\left( {3x} \right) - 16\left( 5 \right) - 10\left( {4x} \right) - 10\left( { - 8} \right) = 40\]

\[ \Rightarrow 48x - 80 - 40x + 80 = 40\]

Now we will keep all the terms with \[x\] on the LHS of the equation and all the constants on the RHS of the equation. Therefore, we get

\[ \Rightarrow 48x - 40x = 40 + 80 - 80\]

Now we will solve this equation to get the value of \[x\].

Adding and subtracting the like terms, we get

\[ \Rightarrow 8x = 40\]

Dividing both sides by 8, we get

\[ \Rightarrow x = \dfrac{{40}}{8}\]

\[ \Rightarrow x = 5\]

In the similar manner, the quadratic equation has 2 solutions because its highest degree is 2. Also, the cubic equations are the equation in which the highest exponent of the variable is 3 and so it has 3 solutions.

We can represent quadratic and cubic equation in the following form:

Quadratic equation: \[a{x^2} + bx + c = 0\]

Cubic equation: \[a{x^3} + b{x^2} + cx + d = 0\]

Students Also Read