Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

1. \(-6x+12=7+x\)
2. \(-10x-5=-1+7x\)
3. \(8x+11=-8+9x\)
4. \(9x+7=-2-8x\)
5. \(12x-4=-8+x\)
6. \(12x+5=14+x\)
7. \(-8x+3=-13+x\)
8. \(-8x-6=11+9x\)
9. \(4x+3=-1-7x\)
10. \(-x+4=14-5x\)
11. \(-10x+15=-8+7x\)
12. \(11x-12=-14+3x\)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -6x \color{red}{+12}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+12}\color{blue}{-12-x } & = & 7 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 7 \color{blue}{-12} \\\Leftrightarrow &-7x & = &-5\\\Leftrightarrow & \color{red}{-7}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-5}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{5}{7} } & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{-5}& = & -1 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{-5}\color{blue}{+5-7x } & = & -1 \color{red}{ +7x }\color{blue}{+5-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & -1 \color{blue}{+5} \\\Leftrightarrow &-17x & = &4\\\Leftrightarrow & \color{red}{-17}x & = &4\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{4}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{17} } & & \\ & V = \left\{ \frac{-4}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & 8x \color{red}{+11}& = & -8 \color{red}{ +9x } \\\Leftrightarrow & 8x \color{red}{+11}\color{blue}{-11-9x } & = & -8 \color{red}{ +9x }\color{blue}{-11-9x } \\\Leftrightarrow & 8x \color{blue}{-9x } & = & -8 \color{blue}{-11} \\\Leftrightarrow &-x & = &-19\\\Leftrightarrow & \color{red}{-}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-19}{-1} \\\Leftrightarrow & \color{green}{ x = 19 } & & \\ & V = \left\{ 19 \right\} & \\\end{align}\)
4. \(\begin{align} & 9x \color{red}{+7}& = & -2 \color{red}{ -8x } \\\Leftrightarrow & 9x \color{red}{+7}\color{blue}{-7+8x } & = & -2 \color{red}{ -8x }\color{blue}{-7+8x } \\\Leftrightarrow & 9x \color{blue}{+8x } & = & -2 \color{blue}{-7} \\\Leftrightarrow &17x & = &-9\\\Leftrightarrow & \color{red}{17}x & = &-9\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-9}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{17} } & & \\ & V = \left\{ \frac{-9}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{-4}& = & -8 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-4}\color{blue}{+4-x } & = & -8 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -8 \color{blue}{+4} \\\Leftrightarrow &11x & = &-4\\\Leftrightarrow & \color{red}{11}x & = &-4\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-4}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{11} } & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & 12x \color{red}{+5}& = & 14 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+5}\color{blue}{-5-x } & = & 14 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 14 \color{blue}{-5} \\\Leftrightarrow &11x & = &9\\\Leftrightarrow & \color{red}{11}x & = &9\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{9}{11} \\\Leftrightarrow & \color{green}{ x = \frac{9}{11} } & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & -8x \color{red}{+3}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+3}\color{blue}{-3-x } & = & -13 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -13 \color{blue}{-3} \\\Leftrightarrow &-9x & = &-16\\\Leftrightarrow & \color{red}{-9}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-16}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{16}{9} } & & \\ & V = \left\{ \frac{16}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{-6}& = & 11 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-6}\color{blue}{+6-9x } & = & 11 \color{red}{ +9x }\color{blue}{+6-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & 11 \color{blue}{+6} \\\Leftrightarrow &-17x & = &17\\\Leftrightarrow & \color{red}{-17}x & = &17\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{17}{-17} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
9. \(\begin{align} & 4x \color{red}{+3}& = & -1 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{+3}\color{blue}{-3+7x } & = & -1 \color{red}{ -7x }\color{blue}{-3+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & -1 \color{blue}{-3} \\\Leftrightarrow &11x & = &-4\\\Leftrightarrow & \color{red}{11}x & = &-4\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-4}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{11} } & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{+4}& = & 14 \color{red}{ -5x } \\\Leftrightarrow & -x \color{red}{+4}\color{blue}{-4+5x } & = & 14 \color{red}{ -5x }\color{blue}{-4+5x } \\\Leftrightarrow & -x \color{blue}{+5x } & = & 14 \color{blue}{-4} \\\Leftrightarrow &4x & = &10\\\Leftrightarrow & \color{red}{4}x & = &10\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{10}{4} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{+15}& = & -8 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+15}\color{blue}{-15-7x } & = & -8 \color{red}{ +7x }\color{blue}{-15-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & -8 \color{blue}{-15} \\\Leftrightarrow &-17x & = &-23\\\Leftrightarrow & \color{red}{-17}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-23}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{23}{17} } & & \\ & V = \left\{ \frac{23}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{-12}& = & -14 \color{red}{ +3x } \\\Leftrightarrow & 11x \color{red}{-12}\color{blue}{+12-3x } & = & -14 \color{red}{ +3x }\color{blue}{+12-3x } \\\Leftrightarrow & 11x \color{blue}{-3x } & = & -14 \color{blue}{+12} \\\Leftrightarrow &8x & = &-2\\\Leftrightarrow & \color{red}{8}x & = &-2\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-2}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)