Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -x \color{red}{+7}& = & -2 \color{red}{ +4x } \\\Leftrightarrow & -x \color{red}{+7}\color{blue}{-7-4x } & = & -2 \color{red}{ +4x }\color{blue}{-7-4x } \\\Leftrightarrow & -x \color{blue}{-4x } & = & -2 \color{blue}{-7} \\\Leftrightarrow &-5x & = &-9\\\Leftrightarrow & \color{red}{-5}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-9}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{9}{5} } & & \\ & V = \left\{ \frac{9}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -11x \color{red}{+2}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+2}\color{blue}{-2-x } & = & -1 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -1 \color{blue}{-2} \\\Leftrightarrow &-12x & = &-3\\\Leftrightarrow & \color{red}{-12}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-3}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{-14}& = & -7 \color{red}{ +2x } \\\Leftrightarrow & 11x \color{red}{-14}\color{blue}{+14-2x } & = & -7 \color{red}{ +2x }\color{blue}{+14-2x } \\\Leftrightarrow & 11x \color{blue}{-2x } & = & -7 \color{blue}{+14} \\\Leftrightarrow &9x & = &7\\\Leftrightarrow & \color{red}{9}x & = &7\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{7}{9} \\\Leftrightarrow & \color{green}{ x = \frac{7}{9} } & & \\ & V = \left\{ \frac{7}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & -3x \color{red}{-3}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-3}\color{blue}{+3-x } & = & 14 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 14 \color{blue}{+3} \\\Leftrightarrow &-4x & = &17\\\Leftrightarrow & \color{red}{-4}x & = &17\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{17}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{4} } & & \\ & V = \left\{ \frac{-17}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & 2x \color{red}{-12}& = & 8 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-12}\color{blue}{+12-x } & = & 8 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 8 \color{blue}{+12} \\\Leftrightarrow &x & = &20\\\Leftrightarrow & \color{red}{}x & = &20\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 20 \\\Leftrightarrow & \color{green}{ x = 20 } & & \\ & V = \left\{ 20 \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{+7}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+7}\color{blue}{-7-x } & = & 8 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 8 \color{blue}{-7} \\\Leftrightarrow &-12x & = &1\\\Leftrightarrow & \color{red}{-12}x & = &1\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{1}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{12} } & & \\ & V = \left\{ \frac{-1}{12} \right\} & \\\end{align}\)
7. \(\begin{align} & -7x \color{red}{+11}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+11}\color{blue}{-11-x } & = & -14 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -14 \color{blue}{-11} \\\Leftrightarrow &-8x & = &-25\\\Leftrightarrow & \color{red}{-8}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-25}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{25}{8} } & & \\ & V = \left\{ \frac{25}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{+11}& = & -1 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+11}\color{blue}{-11-7x } & = & -1 \color{red}{ +7x }\color{blue}{-11-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & -1 \color{blue}{-11} \\\Leftrightarrow &-17x & = &-12\\\Leftrightarrow & \color{red}{-17}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-12}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{12}{17} } & & \\ & V = \left\{ \frac{12}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{-11}& = & 13 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-11}\color{blue}{+11-7x } & = & 13 \color{red}{ +7x }\color{blue}{+11-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & 13 \color{blue}{+11} \\\Leftrightarrow &-13x & = &24\\\Leftrightarrow & \color{red}{-13}x & = &24\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{24}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{13} } & & \\ & V = \left\{ \frac{-24}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{-9}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{-9}\color{blue}{+9-x } & = & -3 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & -3 \color{blue}{+9} \\\Leftrightarrow &9x & = &6\\\Leftrightarrow & \color{red}{9}x & = &6\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{6}{9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -x \color{red}{+1}& = & 13 \color{red}{ -3x } \\\Leftrightarrow & -x \color{red}{+1}\color{blue}{-1+3x } & = & 13 \color{red}{ -3x }\color{blue}{-1+3x } \\\Leftrightarrow & -x \color{blue}{+3x } & = & 13 \color{blue}{-1} \\\Leftrightarrow &2x & = &12\\\Leftrightarrow & \color{red}{2}x & = &12\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{12}{2} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
12. \(\begin{align} & 8x \color{red}{-7}& = & -14 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{-7}\color{blue}{+7+7x } & = & -14 \color{red}{ -7x }\color{blue}{+7+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & -14 \color{blue}{+7} \\\Leftrightarrow &15x & = &-7\\\Leftrightarrow & \color{red}{15}x & = &-7\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-7}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{15} } & & \\ & V = \left\{ \frac{-7}{15} \right\} & \\\end{align}\)