Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 6x \color{red}{+6}& = & 7 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+6}\color{blue}{-6-x } & = & 7 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 7 \color{blue}{-6} \\\Leftrightarrow &5x & = &1\\\Leftrightarrow & \color{red}{5}x & = &1\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{1}{5} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{+4}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+4}\color{blue}{-4-x } & = & -6 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -6 \color{blue}{-4} \\\Leftrightarrow &-11x & = &-10\\\Leftrightarrow & \color{red}{-11}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-10}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{10}{11} } & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{-9}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-9}\color{blue}{+9-x } & = & -11 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -11 \color{blue}{+9} \\\Leftrightarrow &-14x & = &-2\\\Leftrightarrow & \color{red}{-14}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-2}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{-12}& = & -15 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{-12}\color{blue}{+12+7x } & = & -15 \color{red}{ -7x }\color{blue}{+12+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & -15 \color{blue}{+12} \\\Leftrightarrow &22x & = &-3\\\Leftrightarrow & \color{red}{22}x & = &-3\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-3}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{22} } & & \\ & V = \left\{ \frac{-3}{22} \right\} & \\\end{align}\)
5. \(\begin{align} & 15x \color{red}{+7}& = & 5 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{+7}\color{blue}{-7+2x } & = & 5 \color{red}{ -2x }\color{blue}{-7+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & 5 \color{blue}{-7} \\\Leftrightarrow &17x & = &-2\\\Leftrightarrow & \color{red}{17}x & = &-2\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-2}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{17} } & & \\ & V = \left\{ \frac{-2}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & 9x \color{red}{-8}& = & 2 \color{red}{ -11x } \\\Leftrightarrow & 9x \color{red}{-8}\color{blue}{+8+11x } & = & 2 \color{red}{ -11x }\color{blue}{+8+11x } \\\Leftrightarrow & 9x \color{blue}{+11x } & = & 2 \color{blue}{+8} \\\Leftrightarrow &20x & = &10\\\Leftrightarrow & \color{red}{20}x & = &10\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{10}{20} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & 10x \color{red}{+8}& = & 6 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{+8}\color{blue}{-8-x } & = & 6 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & 6 \color{blue}{-8} \\\Leftrightarrow &9x & = &-2\\\Leftrightarrow & \color{red}{9}x & = &-2\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-2}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{9} } & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & 6x \color{red}{-3}& = & -11 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-3}\color{blue}{+3-x } & = & -11 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & -11 \color{blue}{+3} \\\Leftrightarrow &5x & = &-8\\\Leftrightarrow & \color{red}{5}x & = &-8\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-8}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{5} } & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -9x \color{red}{+1}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+1}\color{blue}{-1-x } & = & 9 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 9 \color{blue}{-1} \\\Leftrightarrow &-10x & = &8\\\Leftrightarrow & \color{red}{-10}x & = &8\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{8}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -3x \color{red}{-6}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-6}\color{blue}{+6-x } & = & 13 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 13 \color{blue}{+6} \\\Leftrightarrow &-4x & = &19\\\Leftrightarrow & \color{red}{-4}x & = &19\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{19}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{4} } & & \\ & V = \left\{ \frac{-19}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & 2x \color{red}{+10}& = & 1 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+10}\color{blue}{-10-x } & = & 1 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 1 \color{blue}{-10} \\\Leftrightarrow &x & = &-9\\\Leftrightarrow & \color{red}{}x & = &-9\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -9 \\\Leftrightarrow & \color{green}{ x = -9 } & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
12. \(\begin{align} & -10x \color{red}{+13}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+13}\color{blue}{-13-x } & = & -15 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -15 \color{blue}{-13} \\\Leftrightarrow &-11x & = &-28\\\Leftrightarrow & \color{red}{-11}x & = &-28\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-28}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{28}{11} } & & \\ & V = \left\{ \frac{28}{11} \right\} & \\\end{align}\)