Question

CHECKING SOLUTIONS OF INEQUALTTIES Check whether the given number is a solution of the inequality. $$a(3 a+2)>50 ; 4$$

Short answer

Yes, the number 4 is indeed a solution to the given inequality.

Step-by-step solution

Identify the Inequality

The inequality provided in the problem is \(a(3 a+2)>50\). It is in the form of \(ax^2 + bx > c\). Here, \(a\), \(b\), \(c\) are the coefficients and \(x\) is the variable.

Substitution

The given number, which is 4, replaces the variable 'a' in the inequality. So the inequality becomes: \(4(3*4+2) > 50\).

Solve

Now, solve the equation by doing the arithmetic to check whether the inequality is correct. First, calculate the expression in the brackets which is \(3*4 + 2 = 14\). Multiply 4 with 14: \(4*14 = 56\). So, \(56 > 50\). The inequality does hold true.