Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -6x \color{red}{-15}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-15}\color{blue}{+15-x } & = & 6 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 6 \color{blue}{+15} \\\Leftrightarrow &-7x & = &21\\\Leftrightarrow & \color{red}{-7}x & = &21\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{21}{-7} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{-7}& = & 8 \color{red}{ +9x } \\\Leftrightarrow & 8x \color{red}{-7}\color{blue}{+7-9x } & = & 8 \color{red}{ +9x }\color{blue}{+7-9x } \\\Leftrightarrow & 8x \color{blue}{-9x } & = & 8 \color{blue}{+7} \\\Leftrightarrow &-x & = &15\\\Leftrightarrow & \color{red}{-}x & = &15\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{15}{-1} \\\Leftrightarrow & \color{green}{ x = -15 } & & \\ & V = \left\{ -15 \right\} & \\\end{align}\)
3. \(\begin{align} & 3x \color{red}{-1}& = & 13 \color{red}{ +4x } \\\Leftrightarrow & 3x \color{red}{-1}\color{blue}{+1-4x } & = & 13 \color{red}{ +4x }\color{blue}{+1-4x } \\\Leftrightarrow & 3x \color{blue}{-4x } & = & 13 \color{blue}{+1} \\\Leftrightarrow &-x & = &14\\\Leftrightarrow & \color{red}{-}x & = &14\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{14}{-1} \\\Leftrightarrow & \color{green}{ x = -14 } & & \\ & V = \left\{ -14 \right\} & \\\end{align}\)
4. \(\begin{align} & -x \color{red}{+8}& = & -13 \color{red}{ -10x } \\\Leftrightarrow & -x \color{red}{+8}\color{blue}{-8+10x } & = & -13 \color{red}{ -10x }\color{blue}{-8+10x } \\\Leftrightarrow & -x \color{blue}{+10x } & = & -13 \color{blue}{-8} \\\Leftrightarrow &9x & = &-21\\\Leftrightarrow & \color{red}{9}x & = &-21\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-21}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{-6}& = & -14 \color{red}{ +7x } \\\Leftrightarrow & 12x \color{red}{-6}\color{blue}{+6-7x } & = & -14 \color{red}{ +7x }\color{blue}{+6-7x } \\\Leftrightarrow & 12x \color{blue}{-7x } & = & -14 \color{blue}{+6} \\\Leftrightarrow &5x & = &-8\\\Leftrightarrow & \color{red}{5}x & = &-8\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-8}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{5} } & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{+4}& = & 2 \color{red}{ +3x } \\\Leftrightarrow & 8x \color{red}{+4}\color{blue}{-4-3x } & = & 2 \color{red}{ +3x }\color{blue}{-4-3x } \\\Leftrightarrow & 8x \color{blue}{-3x } & = & 2 \color{blue}{-4} \\\Leftrightarrow &5x & = &-2\\\Leftrightarrow & \color{red}{5}x & = &-2\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-2}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 4x \color{red}{+7}& = & -13 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{+7}\color{blue}{-7+7x } & = & -13 \color{red}{ -7x }\color{blue}{-7+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & -13 \color{blue}{-7} \\\Leftrightarrow &11x & = &-20\\\Leftrightarrow & \color{red}{11}x & = &-20\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-20}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{11} } & & \\ & V = \left\{ \frac{-20}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 15x \color{red}{-7}& = & -14 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{-7}\color{blue}{+7+7x } & = & -14 \color{red}{ -7x }\color{blue}{+7+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & -14 \color{blue}{+7} \\\Leftrightarrow &22x & = &-7\\\Leftrightarrow & \color{red}{22}x & = &-7\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-7}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{22} } & & \\ & V = \left\{ \frac{-7}{22} \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{+13}& = & 11 \color{red}{ +13x } \\\Leftrightarrow & 11x \color{red}{+13}\color{blue}{-13-13x } & = & 11 \color{red}{ +13x }\color{blue}{-13-13x } \\\Leftrightarrow & 11x \color{blue}{-13x } & = & 11 \color{blue}{-13} \\\Leftrightarrow &-2x & = &-2\\\Leftrightarrow & \color{red}{-2}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{-2}{-2} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{+11}& = & -8 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+11}\color{blue}{-11+11x } & = & -8 \color{red}{ -11x }\color{blue}{-11+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -8 \color{blue}{-11} \\\Leftrightarrow &23x & = &-19\\\Leftrightarrow & \color{red}{23}x & = &-19\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-19}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{23} } & & \\ & V = \left\{ \frac{-19}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & 11x \color{red}{+15}& = & -15 \color{red}{ -2x } \\\Leftrightarrow & 11x \color{red}{+15}\color{blue}{-15+2x } & = & -15 \color{red}{ -2x }\color{blue}{-15+2x } \\\Leftrightarrow & 11x \color{blue}{+2x } & = & -15 \color{blue}{-15} \\\Leftrightarrow &13x & = &-30\\\Leftrightarrow & \color{red}{13}x & = &-30\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-30}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-30}{13} } & & \\ & V = \left\{ \frac{-30}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & -4x \color{red}{-6}& = & -8 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{-6}\color{blue}{+6-9x } & = & -8 \color{red}{ +9x }\color{blue}{+6-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & -8 \color{blue}{+6} \\\Leftrightarrow &-13x & = &-2\\\Leftrightarrow & \color{red}{-13}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-2}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{2}{13} } & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)