Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{+3}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+3}\color{blue}{-3-x } & = & 6 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 6 \color{blue}{-3} \\\Leftrightarrow &-10x & = &3\\\Leftrightarrow & \color{red}{-10}x & = &3\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{3}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{10} } & & \\ & V = \left\{ \frac{-3}{10} \right\} & \\\end{align}\)
2. \(\begin{align} & -14x \color{red}{-8}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-8}\color{blue}{+8-x } & = & -11 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -11 \color{blue}{+8} \\\Leftrightarrow &-15x & = &-3\\\Leftrightarrow & \color{red}{-15}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-3}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 2x \color{red}{+5}& = & 4 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+5}\color{blue}{-5-x } & = & 4 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 4 \color{blue}{-5} \\\Leftrightarrow &x & = &-1\\\Leftrightarrow & \color{red}{}x & = &-1\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -1 \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{-4}& = & -14 \color{red}{ +11x } \\\Leftrightarrow & 5x \color{red}{-4}\color{blue}{+4-11x } & = & -14 \color{red}{ +11x }\color{blue}{+4-11x } \\\Leftrightarrow & 5x \color{blue}{-11x } & = & -14 \color{blue}{+4} \\\Leftrightarrow &-6x & = &-10\\\Leftrightarrow & \color{red}{-6}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-10}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 14x \color{red}{+8}& = & 4 \color{red}{ -11x } \\\Leftrightarrow & 14x \color{red}{+8}\color{blue}{-8+11x } & = & 4 \color{red}{ -11x }\color{blue}{-8+11x } \\\Leftrightarrow & 14x \color{blue}{+11x } & = & 4 \color{blue}{-8} \\\Leftrightarrow &25x & = &-4\\\Leftrightarrow & \color{red}{25}x & = &-4\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{-4}{25} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{25} } & & \\ & V = \left\{ \frac{-4}{25} \right\} & \\\end{align}\)
6. \(\begin{align} & 2x \color{red}{+3}& = & -13 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+3}\color{blue}{-3-x } & = & -13 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -13 \color{blue}{-3} \\\Leftrightarrow &x & = &-16\\\Leftrightarrow & \color{red}{}x & = &-16\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -16 \\\Leftrightarrow & \color{green}{ x = -16 } & & \\ & V = \left\{ -16 \right\} & \\\end{align}\)
7. \(\begin{align} & 4x \color{red}{+8}& = & -10 \color{red}{ +9x } \\\Leftrightarrow & 4x \color{red}{+8}\color{blue}{-8-9x } & = & -10 \color{red}{ +9x }\color{blue}{-8-9x } \\\Leftrightarrow & 4x \color{blue}{-9x } & = & -10 \color{blue}{-8} \\\Leftrightarrow &-5x & = &-18\\\Leftrightarrow & \color{red}{-5}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-18}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{18}{5} } & & \\ & V = \left\{ \frac{18}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -2x \color{red}{-3}& = & -4 \color{red}{ +7x } \\\Leftrightarrow & -2x \color{red}{-3}\color{blue}{+3-7x } & = & -4 \color{red}{ +7x }\color{blue}{+3-7x } \\\Leftrightarrow & -2x \color{blue}{-7x } & = & -4 \color{blue}{+3} \\\Leftrightarrow &-9x & = &-1\\\Leftrightarrow & \color{red}{-9}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-1}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{9} } & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & 12x \color{red}{+10}& = & -11 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+10}\color{blue}{-10-x } & = & -11 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -11 \color{blue}{-10} \\\Leftrightarrow &11x & = &-21\\\Leftrightarrow & \color{red}{11}x & = &-21\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-21}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{11} } & & \\ & V = \left\{ \frac{-21}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{-12}& = & -2 \color{red}{ +6x } \\\Leftrightarrow & -x \color{red}{-12}\color{blue}{+12-6x } & = & -2 \color{red}{ +6x }\color{blue}{+12-6x } \\\Leftrightarrow & -x \color{blue}{-6x } & = & -2 \color{blue}{+12} \\\Leftrightarrow &-7x & = &10\\\Leftrightarrow & \color{red}{-7}x & = &10\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{10}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{7} } & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{-10}& = & 10 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{-10}\color{blue}{+10+3x } & = & 10 \color{red}{ -3x }\color{blue}{+10+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & 10 \color{blue}{+10} \\\Leftrightarrow &13x & = &20\\\Leftrightarrow & \color{red}{13}x & = &20\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{20}{13} \\\Leftrightarrow & \color{green}{ x = \frac{20}{13} } & & \\ & V = \left\{ \frac{20}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & -7x \color{red}{+3}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+3}\color{blue}{-3-x } & = & 11 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 11 \color{blue}{-3} \\\Leftrightarrow &-8x & = &8\\\Leftrightarrow & \color{red}{-8}x & = &8\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{8}{-8} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)