Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -6x \color{red}{-7}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-7}\color{blue}{+7-x } & = & -14 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -14 \color{blue}{+7} \\\Leftrightarrow &-7x & = &-7\\\Leftrightarrow & \color{red}{-7}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-7}{-7} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{-4}& = & -3 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{-4}\color{blue}{+4+7x } & = & -3 \color{red}{ -7x }\color{blue}{+4+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & -3 \color{blue}{+4} \\\Leftrightarrow &19x & = &1\\\Leftrightarrow & \color{red}{19}x & = &1\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{1}{19} \\\Leftrightarrow & \color{green}{ x = \frac{1}{19} } & & \\ & V = \left\{ \frac{1}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{+13}& = & -9 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{+13}\color{blue}{-13+2x } & = & -9 \color{red}{ -2x }\color{blue}{-13+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & -9 \color{blue}{-13} \\\Leftrightarrow &17x & = &-22\\\Leftrightarrow & \color{red}{17}x & = &-22\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-22}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{17} } & & \\ & V = \left\{ \frac{-22}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{-8}& = & 9 \color{red}{ -9x } \\\Leftrightarrow & 5x \color{red}{-8}\color{blue}{+8+9x } & = & 9 \color{red}{ -9x }\color{blue}{+8+9x } \\\Leftrightarrow & 5x \color{blue}{+9x } & = & 9 \color{blue}{+8} \\\Leftrightarrow &14x & = &17\\\Leftrightarrow & \color{red}{14}x & = &17\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{17}{14} \\\Leftrightarrow & \color{green}{ x = \frac{17}{14} } & & \\ & V = \left\{ \frac{17}{14} \right\} & \\\end{align}\)
5. \(\begin{align} & 13x \color{red}{+6}& = & 13 \color{red}{ +10x } \\\Leftrightarrow & 13x \color{red}{+6}\color{blue}{-6-10x } & = & 13 \color{red}{ +10x }\color{blue}{-6-10x } \\\Leftrightarrow & 13x \color{blue}{-10x } & = & 13 \color{blue}{-6} \\\Leftrightarrow &3x & = &7\\\Leftrightarrow & \color{red}{3}x & = &7\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{7}{3} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & 7x \color{red}{-9}& = & 15 \color{red}{ +2x } \\\Leftrightarrow & 7x \color{red}{-9}\color{blue}{+9-2x } & = & 15 \color{red}{ +2x }\color{blue}{+9-2x } \\\Leftrightarrow & 7x \color{blue}{-2x } & = & 15 \color{blue}{+9} \\\Leftrightarrow &5x & = &24\\\Leftrightarrow & \color{red}{5}x & = &24\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{24}{5} \\\Leftrightarrow & \color{green}{ x = \frac{24}{5} } & & \\ & V = \left\{ \frac{24}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{-11}& = & -1 \color{red}{ +4x } \\\Leftrightarrow & -3x \color{red}{-11}\color{blue}{+11-4x } & = & -1 \color{red}{ +4x }\color{blue}{+11-4x } \\\Leftrightarrow & -3x \color{blue}{-4x } & = & -1 \color{blue}{+11} \\\Leftrightarrow &-7x & = &10\\\Leftrightarrow & \color{red}{-7}x & = &10\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{10}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{7} } & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{+13}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+13}\color{blue}{-13-x } & = & 15 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 15 \color{blue}{-13} \\\Leftrightarrow &-11x & = &2\\\Leftrightarrow & \color{red}{-11}x & = &2\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{2}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{11} } & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{-7}& = & -8 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{-7}\color{blue}{+7+13x } & = & -8 \color{red}{ -13x }\color{blue}{+7+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & -8 \color{blue}{+7} \\\Leftrightarrow &22x & = &-1\\\Leftrightarrow & \color{red}{22}x & = &-1\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-1}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{22} } & & \\ & V = \left\{ \frac{-1}{22} \right\} & \\\end{align}\)
10. \(\begin{align} & -7x \color{red}{-10}& = & 10 \color{red}{ +8x } \\\Leftrightarrow & -7x \color{red}{-10}\color{blue}{+10-8x } & = & 10 \color{red}{ +8x }\color{blue}{+10-8x } \\\Leftrightarrow & -7x \color{blue}{-8x } & = & 10 \color{blue}{+10} \\\Leftrightarrow &-15x & = &20\\\Leftrightarrow & \color{red}{-15}x & = &20\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{20}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -4x \color{red}{+15}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+15}\color{blue}{-15-x } & = & 12 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 12 \color{blue}{-15} \\\Leftrightarrow &-5x & = &-3\\\Leftrightarrow & \color{red}{-5}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-3}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{+2}& = & 15 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+2}\color{blue}{-2-x } & = & 15 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 15 \color{blue}{-2} \\\Leftrightarrow &x & = &13\\\Leftrightarrow & \color{red}{}x & = &13\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 13 \\\Leftrightarrow & \color{green}{ x = 13 } & & \\ & V = \left\{ 13 \right\} & \\\end{align}\)