Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 12x \color{red}{+2}& = & 1 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+2}\color{blue}{-2+11x } & = & 1 \color{red}{ -11x }\color{blue}{-2+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 1 \color{blue}{-2} \\\Leftrightarrow &23x & = &-1\\\Leftrightarrow & \color{red}{23}x & = &-1\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-1}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{23} } & & \\ & V = \left\{ \frac{-1}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & -5x \color{red}{+2}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+2}\color{blue}{-2-x } & = & -2 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -2 \color{blue}{-2} \\\Leftrightarrow &-6x & = &-4\\\Leftrightarrow & \color{red}{-6}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-4}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & -7x \color{red}{-2}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-2}\color{blue}{+2-x } & = & 11 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 11 \color{blue}{+2} \\\Leftrightarrow &-8x & = &13\\\Leftrightarrow & \color{red}{-8}x & = &13\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{13}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{8} } & & \\ & V = \left\{ \frac{-13}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{+12}& = & 9 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+12}\color{blue}{-12+5x } & = & 9 \color{red}{ -5x }\color{blue}{-12+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & 9 \color{blue}{-12} \\\Leftrightarrow &11x & = &-3\\\Leftrightarrow & \color{red}{11}x & = &-3\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-3}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{11} } & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 7x \color{red}{+15}& = & -2 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{+15}\color{blue}{-15+13x } & = & -2 \color{red}{ -13x }\color{blue}{-15+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & -2 \color{blue}{-15} \\\Leftrightarrow &20x & = &-17\\\Leftrightarrow & \color{red}{20}x & = &-17\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{-17}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{20} } & & \\ & V = \left\{ \frac{-17}{20} \right\} & \\\end{align}\)
6. \(\begin{align} & 4x \color{red}{+14}& = & -11 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{+14}\color{blue}{-14-x } & = & -11 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & -11 \color{blue}{-14} \\\Leftrightarrow &3x & = &-25\\\Leftrightarrow & \color{red}{3}x & = &-25\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-25}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{3} } & & \\ & V = \left\{ \frac{-25}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 5x \color{red}{+2}& = & 6 \color{red}{ -4x } \\\Leftrightarrow & 5x \color{red}{+2}\color{blue}{-2+4x } & = & 6 \color{red}{ -4x }\color{blue}{-2+4x } \\\Leftrightarrow & 5x \color{blue}{+4x } & = & 6 \color{blue}{-2} \\\Leftrightarrow &9x & = &4\\\Leftrightarrow & \color{red}{9}x & = &4\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{4}{9} \\\Leftrightarrow & \color{green}{ x = \frac{4}{9} } & & \\ & V = \left\{ \frac{4}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & x \color{red}{+9}& = & 13 \color{red}{ -3x } \\\Leftrightarrow & x \color{red}{+9}\color{blue}{-9+3x } & = & 13 \color{red}{ -3x }\color{blue}{-9+3x } \\\Leftrightarrow & x \color{blue}{+3x } & = & 13 \color{blue}{-9} \\\Leftrightarrow &4x & = &4\\\Leftrightarrow & \color{red}{4}x & = &4\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{4}{4} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
9. \(\begin{align} & 3x \color{red}{+4}& = & 13 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{+4}\color{blue}{-4+8x } & = & 13 \color{red}{ -8x }\color{blue}{-4+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & 13 \color{blue}{-4} \\\Leftrightarrow &11x & = &9\\\Leftrightarrow & \color{red}{11}x & = &9\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{9}{11} \\\Leftrightarrow & \color{green}{ x = \frac{9}{11} } & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & -12x \color{red}{-2}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-2}\color{blue}{+2-x } & = & 4 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 4 \color{blue}{+2} \\\Leftrightarrow &-13x & = &6\\\Leftrightarrow & \color{red}{-13}x & = &6\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{6}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{13} } & & \\ & V = \left\{ \frac{-6}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & -8x \color{red}{+5}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+5}\color{blue}{-5-x } & = & 4 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 4 \color{blue}{-5} \\\Leftrightarrow &-9x & = &-1\\\Leftrightarrow & \color{red}{-9}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-1}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{9} } & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{+11}& = & 13 \color{red}{ +7x } \\\Leftrightarrow & 13x \color{red}{+11}\color{blue}{-11-7x } & = & 13 \color{red}{ +7x }\color{blue}{-11-7x } \\\Leftrightarrow & 13x \color{blue}{-7x } & = & 13 \color{blue}{-11} \\\Leftrightarrow &6x & = &2\\\Leftrightarrow & \color{red}{6}x & = &2\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{2}{6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)