Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 11x \color{red}{-10}& = & -6 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{-10}\color{blue}{+10+13x } & = & -6 \color{red}{ -13x }\color{blue}{+10+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & -6 \color{blue}{+10} \\\Leftrightarrow &24x & = &4\\\Leftrightarrow & \color{red}{24}x & = &4\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{4}{24} \\\Leftrightarrow & \color{green}{ x = \frac{1}{6} } & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)
2. \(\begin{align} & 7x \color{red}{-14}& = & -3 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{-14}\color{blue}{+14+13x } & = & -3 \color{red}{ -13x }\color{blue}{+14+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & -3 \color{blue}{+14} \\\Leftrightarrow &20x & = &11\\\Leftrightarrow & \color{red}{20}x & = &11\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{11}{20} \\\Leftrightarrow & \color{green}{ x = \frac{11}{20} } & & \\ & V = \left\{ \frac{11}{20} \right\} & \\\end{align}\)
3. \(\begin{align} & -3x \color{red}{+7}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+7}\color{blue}{-7-x } & = & -9 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -9 \color{blue}{-7} \\\Leftrightarrow &-4x & = &-16\\\Leftrightarrow & \color{red}{-4}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-16}{-4} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
4. \(\begin{align} & -4x \color{red}{+14}& = & 13 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{+14}\color{blue}{-14-13x } & = & 13 \color{red}{ +13x }\color{blue}{-14-13x } \\\Leftrightarrow & -4x \color{blue}{-13x } & = & 13 \color{blue}{-14} \\\Leftrightarrow &-17x & = &-1\\\Leftrightarrow & \color{red}{-17}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-1}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{1}{17} } & & \\ & V = \left\{ \frac{1}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & -3x \color{red}{+13}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+13}\color{blue}{-13-x } & = & 14 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 14 \color{blue}{-13} \\\Leftrightarrow &-4x & = &1\\\Leftrightarrow & \color{red}{-4}x & = &1\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{1}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & -5x \color{red}{-8}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-8}\color{blue}{+8-x } & = & -14 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -14 \color{blue}{+8} \\\Leftrightarrow &-6x & = &-6\\\Leftrightarrow & \color{red}{-6}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-6}{-6} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
7. \(\begin{align} & -9x \color{red}{+3}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+3}\color{blue}{-3-x } & = & 5 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 5 \color{blue}{-3} \\\Leftrightarrow &-10x & = &2\\\Leftrightarrow & \color{red}{-10}x & = &2\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{2}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 10x \color{red}{-2}& = & 6 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{-2}\color{blue}{+2-7x } & = & 6 \color{red}{ +7x }\color{blue}{+2-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & 6 \color{blue}{+2} \\\Leftrightarrow &3x & = &8\\\Leftrightarrow & \color{red}{3}x & = &8\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{8}{3} \\\Leftrightarrow & \color{green}{ x = \frac{8}{3} } & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 10x \color{red}{-2}& = & -1 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{-2}\color{blue}{+2-7x } & = & -1 \color{red}{ +7x }\color{blue}{+2-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & -1 \color{blue}{+2} \\\Leftrightarrow &3x & = &1\\\Leftrightarrow & \color{red}{3}x & = &1\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{1}{3} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -3x \color{red}{-11}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-11}\color{blue}{+11-x } & = & -13 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -13 \color{blue}{+11} \\\Leftrightarrow &-4x & = &-2\\\Leftrightarrow & \color{red}{-4}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-2}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & 8x \color{red}{-15}& = & -2 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{-15}\color{blue}{+15-x } & = & -2 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & -2 \color{blue}{+15} \\\Leftrightarrow &7x & = &13\\\Leftrightarrow & \color{red}{7}x & = &13\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{13}{7} \\\Leftrightarrow & \color{green}{ x = \frac{13}{7} } & & \\ & V = \left\{ \frac{13}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{+14}& = & -4 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+14}\color{blue}{-14-x } & = & -4 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -4 \color{blue}{-14} \\\Leftrightarrow &x & = &-18\\\Leftrightarrow & \color{red}{}x & = &-18\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -18 \\\Leftrightarrow & \color{green}{ x = -18 } & & \\ & V = \left\{ -18 \right\} & \\\end{align}\)