Video: AQA GCSE Mathematics Foundation Tier Pack 3 • Paper 3 • Question 4

Solve −4𝑡 = 20. Circle your answer. [A] 𝑡 = −1/5 [B] 𝑡 = 24 [C] 𝑡 =5 [D] 𝑡 = −5

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Video Transcript

Solve negative four 𝑡 equals 20. Circle your answer. Is it 𝑡 is equal to negative one-fifth, 𝑡 equals 24, 𝑡 equals five, or 𝑡 equals negative five?

We can solve this equation using one step. We do this by dividing both sides of the equation by negative four. This is because negative four 𝑡 means negative four multiplied by 𝑡. The opposite or inverse operation to multiplying by negative four is dividing by negative four. When we divide two positive numbers, we get a positive answer. Dividing a positive by a negative or a negative by a positive gives us a negative answer. And dividing a negative number by another negative number gives us a positive answer.

Using this bottom rule, the left-hand side of the equation becomes positive one 𝑡 as negative four 𝑡 divided by negative four is equal to positive one 𝑡. Dividing four by four gives us one. And the two negative signs become a positive. One 𝑡 can just be written as 𝑡. 20 divided by negative four is equal to negative five as 20 divided by four is five. And dividing a positive number by a negative number gives a negative answer. The solution to the equation negative four 𝑡 equals 20 is 𝑡 equals negative five. So we need to circle this answer.

We can check our answer by substituting this value of 𝑡 back into the original equation. Negative four multiplied by 𝑡 equals 20. Substituting in 𝑡 equals negative five gives us negative four multiplied by negative five. This is equal to 20 as multiplying two negative numbers gives us a positive answer. And four multiplied by five is 20.

Of the four options, 𝑡 equals negative one-fifth, 24, five, and negative five, the correct answer is negative five. Another way of thinking about this problem is to work out what we need to multiply negative four by to give us 20. The answer to this is negative five.

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