Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{-6}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-6}\color{blue}{+6-x } & = & -14 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -14 \color{blue}{+6} \\\Leftrightarrow &-4x & = &-8\\\Leftrightarrow & \color{red}{-4}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-8}{-4} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{-15}& = & -1 \color{red}{ +11x } \\\Leftrightarrow & 15x \color{red}{-15}\color{blue}{+15-11x } & = & -1 \color{red}{ +11x }\color{blue}{+15-11x } \\\Leftrightarrow & 15x \color{blue}{-11x } & = & -1 \color{blue}{+15} \\\Leftrightarrow &4x & = &14\\\Leftrightarrow & \color{red}{4}x & = &14\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{14}{4} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & 2x \color{red}{+7}& = & -3 \color{red}{ +13x } \\\Leftrightarrow & 2x \color{red}{+7}\color{blue}{-7-13x } & = & -3 \color{red}{ +13x }\color{blue}{-7-13x } \\\Leftrightarrow & 2x \color{blue}{-13x } & = & -3 \color{blue}{-7} \\\Leftrightarrow &-11x & = &-10\\\Leftrightarrow & \color{red}{-11}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-10}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{10}{11} } & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & 8x \color{red}{-4}& = & -10 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{-4}\color{blue}{+4-x } & = & -10 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & -10 \color{blue}{+4} \\\Leftrightarrow &7x & = &-6\\\Leftrightarrow & \color{red}{7}x & = &-6\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-6}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{7} } & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -4x \color{red}{+1}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+1}\color{blue}{-1-x } & = & 14 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 14 \color{blue}{-1} \\\Leftrightarrow &-5x & = &13\\\Leftrightarrow & \color{red}{-5}x & = &13\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{13}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{5} } & & \\ & V = \left\{ \frac{-13}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 2x \color{red}{+2}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+2}\color{blue}{-2-x } & = & -3 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -3 \color{blue}{-2} \\\Leftrightarrow &x & = &-5\\\Leftrightarrow & \color{red}{}x & = &-5\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -5 \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
7. \(\begin{align} & -7x \color{red}{+3}& = & 11 \color{red}{ +8x } \\\Leftrightarrow & -7x \color{red}{+3}\color{blue}{-3-8x } & = & 11 \color{red}{ +8x }\color{blue}{-3-8x } \\\Leftrightarrow & -7x \color{blue}{-8x } & = & 11 \color{blue}{-3} \\\Leftrightarrow &-15x & = &8\\\Leftrightarrow & \color{red}{-15}x & = &8\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{8}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{15} } & & \\ & V = \left\{ \frac{-8}{15} \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{-8}& = & -15 \color{red}{ +4x } \\\Leftrightarrow & 5x \color{red}{-8}\color{blue}{+8-4x } & = & -15 \color{red}{ +4x }\color{blue}{+8-4x } \\\Leftrightarrow & 5x \color{blue}{-4x } & = & -15 \color{blue}{+8} \\\Leftrightarrow &x & = &-7\\\Leftrightarrow & \color{red}{}x & = &-7\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -7 \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
9. \(\begin{align} & -9x \color{red}{-6}& = & -1 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{-6}\color{blue}{+6-14x } & = & -1 \color{red}{ +14x }\color{blue}{+6-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & -1 \color{blue}{+6} \\\Leftrightarrow &-23x & = &5\\\Leftrightarrow & \color{red}{-23}x & = &5\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{5}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{23} } & & \\ & V = \left\{ \frac{-5}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{+8}& = & -3 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{+8}\color{blue}{-8+13x } & = & -3 \color{red}{ -13x }\color{blue}{-8+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & -3 \color{blue}{-8} \\\Leftrightarrow &23x & = &-11\\\Leftrightarrow & \color{red}{23}x & = &-11\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-11}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{23} } & & \\ & V = \left\{ \frac{-11}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & -11x \color{red}{-14}& = & 6 \color{red}{ +14x } \\\Leftrightarrow & -11x \color{red}{-14}\color{blue}{+14-14x } & = & 6 \color{red}{ +14x }\color{blue}{+14-14x } \\\Leftrightarrow & -11x \color{blue}{-14x } & = & 6 \color{blue}{+14} \\\Leftrightarrow &-25x & = &20\\\Leftrightarrow & \color{red}{-25}x & = &20\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{20}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -6x \color{red}{+5}& = & -14 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+5}\color{blue}{-5-13x } & = & -14 \color{red}{ +13x }\color{blue}{-5-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & -14 \color{blue}{-5} \\\Leftrightarrow &-19x & = &-19\\\Leftrightarrow & \color{red}{-19}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-19}{-19} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)