The equations 2x + 7 = 3 and bx - 10 = -2 have the same solution. What is the value of b?

Question

Accepted Answer

{"content":[{"type":"paragraph","content":[{"marks":[{"type":"bold"}],"text":"Step 1 (Solve the first equation):","type":"text"},{"type":"text","text":" Solve "},{"attrs":{"latex":"2x + 7 = 3"},"type":"math_inline"},{"text":" for ","type":"text"},{"type":"math_inline","attrs":{"latex":"x"}},{"text":":","type":"text"}]},{"attrs":{"latex":"2x = 3 - 7 \implies 2x = -4 \implies x = -2"},"type":"math_block"},{"content":[{"text":"Step 2 (Substitute into the second equation):","type":"text","marks":[{"type":"bold"}]},{"text":" Since both equations have the same solution, substitute ","type":"text"},{"attrs":{"latex":"x = -2"},"type":"math_inline"},{"text":" into ","type":"text"},{"attrs":{"latex":"bx - 10 = -2"},"type":"math_inline"},{"text":":","type":"text"}],"type":"paragraph"},{"attrs":{"latex":"b(-2) - 10 = -2 \implies -2b - 10 = -2"},"type":"math_block"},{"attrs":{"latex":"-2b = -2 + 10 \implies -2b = 8 \implies b = -4"},"type":"math_block"},{"content":[{"marks":[{"type":"bold"}],"text":"Step 3 (Conclusion):","type":"text"},{"text":" The value of ","type":"text"},{"attrs":{"latex":"b"},"type":"math_inline"},{"text":" is exactly ","type":"text"},{"attrs":{"latex":"-4"},"type":"math_inline"},{"text":".","type":"text"}],"type":"paragraph"}],"type":"doc"}

Options:

Guide / Hint

Solution