Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{-2}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-2}\color{blue}{+2-x } & = & 12 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 12 \color{blue}{+2} \\\Leftrightarrow &-14x & = &14\\\Leftrightarrow & \color{red}{-14}x & = &14\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{14}{-14} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
2. \(\begin{align} & 13x \color{red}{-3}& = & 2 \color{red}{ +8x } \\\Leftrightarrow & 13x \color{red}{-3}\color{blue}{+3-8x } & = & 2 \color{red}{ +8x }\color{blue}{+3-8x } \\\Leftrightarrow & 13x \color{blue}{-8x } & = & 2 \color{blue}{+3} \\\Leftrightarrow &5x & = &5\\\Leftrightarrow & \color{red}{5}x & = &5\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{5}{5} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
3. \(\begin{align} & -3x \color{red}{-14}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-14}\color{blue}{+14-x } & = & 4 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 4 \color{blue}{+14} \\\Leftrightarrow &-4x & = &18\\\Leftrightarrow & \color{red}{-4}x & = &18\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{18}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{2} } & & \\ & V = \left\{ \frac{-9}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & -3x \color{red}{+6}& = & 5 \color{red}{ +10x } \\\Leftrightarrow & -3x \color{red}{+6}\color{blue}{-6-10x } & = & 5 \color{red}{ +10x }\color{blue}{-6-10x } \\\Leftrightarrow & -3x \color{blue}{-10x } & = & 5 \color{blue}{-6} \\\Leftrightarrow &-13x & = &-1\\\Leftrightarrow & \color{red}{-13}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-1}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{1}{13} } & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & 11x \color{red}{+14}& = & 6 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{+14}\color{blue}{-14+13x } & = & 6 \color{red}{ -13x }\color{blue}{-14+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & 6 \color{blue}{-14} \\\Leftrightarrow &24x & = &-8\\\Leftrightarrow & \color{red}{24}x & = &-8\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{-8}{24} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & 4x \color{red}{-13}& = & 6 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{-13}\color{blue}{+13+3x } & = & 6 \color{red}{ -3x }\color{blue}{+13+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & 6 \color{blue}{+13} \\\Leftrightarrow &7x & = &19\\\Leftrightarrow & \color{red}{7}x & = &19\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{19}{7} \\\Leftrightarrow & \color{green}{ x = \frac{19}{7} } & & \\ & V = \left\{ \frac{19}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{-15}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-15}\color{blue}{+15-x } & = & -6 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -6 \color{blue}{+15} \\\Leftrightarrow &-11x & = &9\\\Leftrightarrow & \color{red}{-11}x & = &9\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{9}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{11} } & & \\ & V = \left\{ \frac{-9}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 6x \color{red}{+8}& = & 12 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+8}\color{blue}{-8+11x } & = & 12 \color{red}{ -11x }\color{blue}{-8+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 12 \color{blue}{-8} \\\Leftrightarrow &17x & = &4\\\Leftrightarrow & \color{red}{17}x & = &4\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{4}{17} \\\Leftrightarrow & \color{green}{ x = \frac{4}{17} } & & \\ & V = \left\{ \frac{4}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & -7x \color{red}{-11}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-11}\color{blue}{+11-x } & = & 9 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 9 \color{blue}{+11} \\\Leftrightarrow &-8x & = &20\\\Leftrightarrow & \color{red}{-8}x & = &20\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{20}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{-1}& = & 12 \color{red}{ +2x } \\\Leftrightarrow & -x \color{red}{-1}\color{blue}{+1-2x } & = & 12 \color{red}{ +2x }\color{blue}{+1-2x } \\\Leftrightarrow & -x \color{blue}{-2x } & = & 12 \color{blue}{+1} \\\Leftrightarrow &-3x & = &13\\\Leftrightarrow & \color{red}{-3}x & = &13\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{13}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{3} } & & \\ & V = \left\{ \frac{-13}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & 3x \color{red}{-14}& = & -9 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{-14}\color{blue}{+14+8x } & = & -9 \color{red}{ -8x }\color{blue}{+14+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & -9 \color{blue}{+14} \\\Leftrightarrow &11x & = &5\\\Leftrightarrow & \color{red}{11}x & = &5\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{5}{11} \\\Leftrightarrow & \color{green}{ x = \frac{5}{11} } & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & 5x \color{red}{-9}& = & 5 \color{red}{ +8x } \\\Leftrightarrow & 5x \color{red}{-9}\color{blue}{+9-8x } & = & 5 \color{red}{ +8x }\color{blue}{+9-8x } \\\Leftrightarrow & 5x \color{blue}{-8x } & = & 5 \color{blue}{+9} \\\Leftrightarrow &-3x & = &14\\\Leftrightarrow & \color{red}{-3}x & = &14\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{14}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{3} } & & \\ & V = \left\{ \frac{-14}{3} \right\} & \\\end{align}\)