Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -2x \color{red}{-7}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-7}\color{blue}{+7-x } & = & -7 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -7 \color{blue}{+7} \\\Leftrightarrow &-3x & = &0\\\Leftrightarrow & \color{red}{-3}x & = &0\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{0}{-3} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{-15}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-15}\color{blue}{+15-x } & = & -7 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -7 \color{blue}{+15} \\\Leftrightarrow &-3x & = &8\\\Leftrightarrow & \color{red}{-3}x & = &8\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{8}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{3} } & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & -14x \color{red}{-5}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-5}\color{blue}{+5-x } & = & -6 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -6 \color{blue}{+5} \\\Leftrightarrow &-15x & = &-1\\\Leftrightarrow & \color{red}{-15}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-1}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{15} } & & \\ & V = \left\{ \frac{1}{15} \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{-10}& = & 2 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-10}\color{blue}{+10-7x } & = & 2 \color{red}{ +7x }\color{blue}{+10-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & 2 \color{blue}{+10} \\\Leftrightarrow &-13x & = &12\\\Leftrightarrow & \color{red}{-13}x & = &12\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{12}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{13} } & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{-7}& = & -7 \color{red}{ +7x } \\\Leftrightarrow & 9x \color{red}{-7}\color{blue}{+7-7x } & = & -7 \color{red}{ +7x }\color{blue}{+7-7x } \\\Leftrightarrow & 9x \color{blue}{-7x } & = & -7 \color{blue}{+7} \\\Leftrightarrow &2x & = &0\\\Leftrightarrow & \color{red}{2}x & = &0\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{0}{2} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{+11}& = & -6 \color{red}{ +9x } \\\Leftrightarrow & -2x \color{red}{+11}\color{blue}{-11-9x } & = & -6 \color{red}{ +9x }\color{blue}{-11-9x } \\\Leftrightarrow & -2x \color{blue}{-9x } & = & -6 \color{blue}{-11} \\\Leftrightarrow &-11x & = &-17\\\Leftrightarrow & \color{red}{-11}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-17}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{17}{11} } & & \\ & V = \left\{ \frac{17}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & 11x \color{red}{+8}& = & 1 \color{red}{ +6x } \\\Leftrightarrow & 11x \color{red}{+8}\color{blue}{-8-6x } & = & 1 \color{red}{ +6x }\color{blue}{-8-6x } \\\Leftrightarrow & 11x \color{blue}{-6x } & = & 1 \color{blue}{-8} \\\Leftrightarrow &5x & = &-7\\\Leftrightarrow & \color{red}{5}x & = &-7\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-7}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 14x \color{red}{-15}& = & -4 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-15}\color{blue}{+15-x } & = & -4 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -4 \color{blue}{+15} \\\Leftrightarrow &13x & = &11\\\Leftrightarrow & \color{red}{13}x & = &11\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{11}{13} \\\Leftrightarrow & \color{green}{ x = \frac{11}{13} } & & \\ & V = \left\{ \frac{11}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & -8x \color{red}{+10}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+10}\color{blue}{-10-x } & = & 4 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 4 \color{blue}{-10} \\\Leftrightarrow &-9x & = &-6\\\Leftrightarrow & \color{red}{-9}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-6}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{-15}& = & -1 \color{red}{ -15x } \\\Leftrightarrow & -x \color{red}{-15}\color{blue}{+15+15x } & = & -1 \color{red}{ -15x }\color{blue}{+15+15x } \\\Leftrightarrow & -x \color{blue}{+15x } & = & -1 \color{blue}{+15} \\\Leftrightarrow &14x & = &14\\\Leftrightarrow & \color{red}{14}x & = &14\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{14}{14} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
11. \(\begin{align} & 11x \color{red}{+5}& = & 13 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{+5}\color{blue}{-5+13x } & = & 13 \color{red}{ -13x }\color{blue}{-5+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & 13 \color{blue}{-5} \\\Leftrightarrow &24x & = &8\\\Leftrightarrow & \color{red}{24}x & = &8\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{8}{24} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -15x \color{red}{-1}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-1}\color{blue}{+1-x } & = & -14 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -14 \color{blue}{+1} \\\Leftrightarrow &-16x & = &-13\\\Leftrightarrow & \color{red}{-16}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-13}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{13}{16} } & & \\ & V = \left\{ \frac{13}{16} \right\} & \\\end{align}\)