Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -10x \color{red}{-6}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-6}\color{blue}{+6-x } & = & 15 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 15 \color{blue}{+6} \\\Leftrightarrow &-11x & = &21\\\Leftrightarrow & \color{red}{-11}x & = &21\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{21}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{11} } & & \\ & V = \left\{ \frac{-21}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -6x \color{red}{+5}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+5}\color{blue}{-5-x } & = & 7 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 7 \color{blue}{-5} \\\Leftrightarrow &-7x & = &2\\\Leftrightarrow & \color{red}{-7}x & = &2\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{2}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{-2}& = & 10 \color{red}{ +7x } \\\Leftrightarrow & 9x \color{red}{-2}\color{blue}{+2-7x } & = & 10 \color{red}{ +7x }\color{blue}{+2-7x } \\\Leftrightarrow & 9x \color{blue}{-7x } & = & 10 \color{blue}{+2} \\\Leftrightarrow &2x & = &12\\\Leftrightarrow & \color{red}{2}x & = &12\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{12}{2} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
4. \(\begin{align} & 8x \color{red}{-11}& = & 2 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{-11}\color{blue}{+11+7x } & = & 2 \color{red}{ -7x }\color{blue}{+11+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & 2 \color{blue}{+11} \\\Leftrightarrow &15x & = &13\\\Leftrightarrow & \color{red}{15}x & = &13\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{13}{15} \\\Leftrightarrow & \color{green}{ x = \frac{13}{15} } & & \\ & V = \left\{ \frac{13}{15} \right\} & \\\end{align}\)
5. \(\begin{align} & 13x \color{red}{+12}& = & 5 \color{red}{ -15x } \\\Leftrightarrow & 13x \color{red}{+12}\color{blue}{-12+15x } & = & 5 \color{red}{ -15x }\color{blue}{-12+15x } \\\Leftrightarrow & 13x \color{blue}{+15x } & = & 5 \color{blue}{-12} \\\Leftrightarrow &28x & = &-7\\\Leftrightarrow & \color{red}{28}x & = &-7\\\Leftrightarrow & \frac{\color{red}{28}x}{ \color{blue}{ 28}} & = & \frac{-7}{28} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & -9x \color{red}{-3}& = & -2 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{-3}\color{blue}{+3-5x } & = & -2 \color{red}{ +5x }\color{blue}{+3-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & -2 \color{blue}{+3} \\\Leftrightarrow &-14x & = &1\\\Leftrightarrow & \color{red}{-14}x & = &1\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{1}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{14} } & & \\ & V = \left\{ \frac{-1}{14} \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{+6}& = & 12 \color{red}{ -9x } \\\Leftrightarrow & x \color{red}{+6}\color{blue}{-6+9x } & = & 12 \color{red}{ -9x }\color{blue}{-6+9x } \\\Leftrightarrow & x \color{blue}{+9x } & = & 12 \color{blue}{-6} \\\Leftrightarrow &10x & = &6\\\Leftrightarrow & \color{red}{10}x & = &6\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{6}{10} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{+6}& = & -5 \color{red}{ +6x } \\\Leftrightarrow & 5x \color{red}{+6}\color{blue}{-6-6x } & = & -5 \color{red}{ +6x }\color{blue}{-6-6x } \\\Leftrightarrow & 5x \color{blue}{-6x } & = & -5 \color{blue}{-6} \\\Leftrightarrow &-x & = &-11\\\Leftrightarrow & \color{red}{-}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-11}{-1} \\\Leftrightarrow & \color{green}{ x = 11 } & & \\ & V = \left\{ 11 \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{+11}& = & -9 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{+11}\color{blue}{-11+2x } & = & -9 \color{red}{ -2x }\color{blue}{-11+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & -9 \color{blue}{-11} \\\Leftrightarrow &17x & = &-20\\\Leftrightarrow & \color{red}{17}x & = &-20\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-20}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{17} } & & \\ & V = \left\{ \frac{-20}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{+10}& = & -10 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+10}\color{blue}{-10+11x } & = & -10 \color{red}{ -11x }\color{blue}{-10+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -10 \color{blue}{-10} \\\Leftrightarrow &23x & = &-20\\\Leftrightarrow & \color{red}{23}x & = &-20\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-20}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{23} } & & \\ & V = \left\{ \frac{-20}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & 12x \color{red}{+15}& = & 9 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+15}\color{blue}{-15+11x } & = & 9 \color{red}{ -11x }\color{blue}{-15+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 9 \color{blue}{-15} \\\Leftrightarrow &23x & = &-6\\\Leftrightarrow & \color{red}{23}x & = &-6\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-6}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{23} } & & \\ & V = \left\{ \frac{-6}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & -6x \color{red}{-15}& = & 3 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-15}\color{blue}{+15-13x } & = & 3 \color{red}{ +13x }\color{blue}{+15-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 3 \color{blue}{+15} \\\Leftrightarrow &-19x & = &18\\\Leftrightarrow & \color{red}{-19}x & = &18\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{18}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{19} } & & \\ & V = \left\{ \frac{-18}{19} \right\} & \\\end{align}\)