Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{+8}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+8}\color{blue}{-8-x } & = & -14 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -14 \color{blue}{-8} \\\Leftrightarrow &x & = &-22\\\Leftrightarrow & \color{red}{}x & = &-22\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -22 \\\Leftrightarrow & \color{green}{ x = -22 } & & \\ & V = \left\{ -22 \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{-4}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-4}\color{blue}{+4-x } & = & 5 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 5 \color{blue}{+4} \\\Leftrightarrow &-14x & = &9\\\Leftrightarrow & \color{red}{-14}x & = &9\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{9}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{14} } & & \\ & V = \left\{ \frac{-9}{14} \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{-3}& = & 5 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{-3}\color{blue}{+3-11x } & = & 5 \color{red}{ +11x }\color{blue}{+3-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & 5 \color{blue}{+3} \\\Leftrightarrow &x & = &8\\\Leftrightarrow & \color{red}{}x & = &8\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 8 \\\Leftrightarrow & \color{green}{ x = 8 } & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
4. \(\begin{align} & -5x \color{red}{-12}& = & 1 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{-12}\color{blue}{+12-6x } & = & 1 \color{red}{ +6x }\color{blue}{+12-6x } \\\Leftrightarrow & -5x \color{blue}{-6x } & = & 1 \color{blue}{+12} \\\Leftrightarrow &-11x & = &13\\\Leftrightarrow & \color{red}{-11}x & = &13\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{13}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{11} } & & \\ & V = \left\{ \frac{-13}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{+8}& = & -1 \color{red}{ +13x } \\\Leftrightarrow & 10x \color{red}{+8}\color{blue}{-8-13x } & = & -1 \color{red}{ +13x }\color{blue}{-8-13x } \\\Leftrightarrow & 10x \color{blue}{-13x } & = & -1 \color{blue}{-8} \\\Leftrightarrow &-3x & = &-9\\\Leftrightarrow & \color{red}{-3}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-9}{-3} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
6. \(\begin{align} & 7x \color{red}{+5}& = & -15 \color{red}{ -10x } \\\Leftrightarrow & 7x \color{red}{+5}\color{blue}{-5+10x } & = & -15 \color{red}{ -10x }\color{blue}{-5+10x } \\\Leftrightarrow & 7x \color{blue}{+10x } & = & -15 \color{blue}{-5} \\\Leftrightarrow &17x & = &-20\\\Leftrightarrow & \color{red}{17}x & = &-20\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-20}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{17} } & & \\ & V = \left\{ \frac{-20}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & 15x \color{red}{+4}& = & -7 \color{red}{ +7x } \\\Leftrightarrow & 15x \color{red}{+4}\color{blue}{-4-7x } & = & -7 \color{red}{ +7x }\color{blue}{-4-7x } \\\Leftrightarrow & 15x \color{blue}{-7x } & = & -7 \color{blue}{-4} \\\Leftrightarrow &8x & = &-11\\\Leftrightarrow & \color{red}{8}x & = &-11\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-11}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{8} } & & \\ & V = \left\{ \frac{-11}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & -3x \color{red}{+8}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+8}\color{blue}{-8-x } & = & -13 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -13 \color{blue}{-8} \\\Leftrightarrow &-4x & = &-21\\\Leftrightarrow & \color{red}{-4}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-21}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{21}{4} } & & \\ & V = \left\{ \frac{21}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{-5}& = & -3 \color{red}{ +4x } \\\Leftrightarrow & 15x \color{red}{-5}\color{blue}{+5-4x } & = & -3 \color{red}{ +4x }\color{blue}{+5-4x } \\\Leftrightarrow & 15x \color{blue}{-4x } & = & -3 \color{blue}{+5} \\\Leftrightarrow &11x & = &2\\\Leftrightarrow & \color{red}{11}x & = &2\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{2}{11} \\\Leftrightarrow & \color{green}{ x = \frac{2}{11} } & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & -2x \color{red}{+8}& = & 1 \color{red}{ +9x } \\\Leftrightarrow & -2x \color{red}{+8}\color{blue}{-8-9x } & = & 1 \color{red}{ +9x }\color{blue}{-8-9x } \\\Leftrightarrow & -2x \color{blue}{-9x } & = & 1 \color{blue}{-8} \\\Leftrightarrow &-11x & = &-7\\\Leftrightarrow & \color{red}{-11}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-7}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{7}{11} } & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{-9}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-9}\color{blue}{+9-x } & = & 11 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 11 \color{blue}{+9} \\\Leftrightarrow &-15x & = &20\\\Leftrightarrow & \color{red}{-15}x & = &20\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{20}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & 14x \color{red}{-3}& = & 14 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-3}\color{blue}{+3+13x } & = & 14 \color{red}{ -13x }\color{blue}{+3+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & 14 \color{blue}{+3} \\\Leftrightarrow &27x & = &17\\\Leftrightarrow & \color{red}{27}x & = &17\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{17}{27} \\\Leftrightarrow & \color{green}{ x = \frac{17}{27} } & & \\ & V = \left\{ \frac{17}{27} \right\} & \\\end{align}\)