Final answer:
To simplify the given expression, we perform the operations inside the parentheses first and then simplify further using the order of operations. The final simplified expression is 129. To solve the equation, we isolate x by dividing both sides of the equation by 7.
Step-by-step explanation:
To simplify the expression 8 squared plus 9 (12 ÷ 3 × 2) minus 7, we first perform the operations inside the parentheses. 12 divided by 3 equals 4, and 4 times 2 equals 8. So the expression becomes 8 squared plus 9 times 8 minus 7. Next, we simplify the squared term. 8 squared means 8 multiplied by itself, which equals 64. So now we have 64 plus 9 times 8 minus 7. We proceed by performing the multiplication: 9 times 8 equals 72. So now the expression is 64 plus 72 minus 7. Finally, we simplify further by performing the addition and subtraction: 64 plus 72 equals 136, and 136 minus 7 equals 129. Therefore, the simplified expression is equal to 129.
To solve the equation 7x = 42, we want to isolate x on one side of the equation. To do this, we divide both sides of the equation by 7 (the coefficient of x): 7x divided by 7 equals x, and 42 divided by 7 equals 6. Therefore, x equals 6.