Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{+11}& = & -1 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{+11}\color{blue}{-11-7x } & = & -1 \color{red}{ +7x }\color{blue}{-11-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -1 \color{blue}{-11} \\\Leftrightarrow &-20x & = &-12\\\Leftrightarrow & \color{red}{-20}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-12}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{+11}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+11}\color{blue}{-11-x } & = & -6 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -6 \color{blue}{-11} \\\Leftrightarrow &-3x & = &-17\\\Leftrightarrow & \color{red}{-3}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-17}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{17}{3} } & & \\ & V = \left\{ \frac{17}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{-14}& = & 11 \color{red}{ +5x } \\\Leftrightarrow & 11x \color{red}{-14}\color{blue}{+14-5x } & = & 11 \color{red}{ +5x }\color{blue}{+14-5x } \\\Leftrightarrow & 11x \color{blue}{-5x } & = & 11 \color{blue}{+14} \\\Leftrightarrow &6x & = &25\\\Leftrightarrow & \color{red}{6}x & = &25\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{25}{6} \\\Leftrightarrow & \color{green}{ x = \frac{25}{6} } & & \\ & V = \left\{ \frac{25}{6} \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{+1}& = & -13 \color{red}{ +9x } \\\Leftrightarrow & 2x \color{red}{+1}\color{blue}{-1-9x } & = & -13 \color{red}{ +9x }\color{blue}{-1-9x } \\\Leftrightarrow & 2x \color{blue}{-9x } & = & -13 \color{blue}{-1} \\\Leftrightarrow &-7x & = &-14\\\Leftrightarrow & \color{red}{-7}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-14}{-7} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
5. \(\begin{align} & 13x \color{red}{+13}& = & 8 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+13}\color{blue}{-13+6x } & = & 8 \color{red}{ -6x }\color{blue}{-13+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & 8 \color{blue}{-13} \\\Leftrightarrow &19x & = &-5\\\Leftrightarrow & \color{red}{19}x & = &-5\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-5}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{19} } & & \\ & V = \left\{ \frac{-5}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & -7x \color{red}{-7}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-7}\color{blue}{+7-x } & = & -6 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -6 \color{blue}{+7} \\\Leftrightarrow &-8x & = &1\\\Leftrightarrow & \color{red}{-8}x & = &1\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{1}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{-12}& = & -1 \color{red}{ -10x } \\\Leftrightarrow & x \color{red}{-12}\color{blue}{+12+10x } & = & -1 \color{red}{ -10x }\color{blue}{+12+10x } \\\Leftrightarrow & x \color{blue}{+10x } & = & -1 \color{blue}{+12} \\\Leftrightarrow &11x & = &11\\\Leftrightarrow & \color{red}{11}x & = &11\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{11}{11} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
8. \(\begin{align} & 12x \color{red}{-7}& = & 10 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{-7}\color{blue}{+7-5x } & = & 10 \color{red}{ +5x }\color{blue}{+7-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & 10 \color{blue}{+7} \\\Leftrightarrow &7x & = &17\\\Leftrightarrow & \color{red}{7}x & = &17\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{17}{7} \\\Leftrightarrow & \color{green}{ x = \frac{17}{7} } & & \\ & V = \left\{ \frac{17}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -7x \color{red}{+2}& = & 12 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{+2}\color{blue}{-2-11x } & = & 12 \color{red}{ +11x }\color{blue}{-2-11x } \\\Leftrightarrow & -7x \color{blue}{-11x } & = & 12 \color{blue}{-2} \\\Leftrightarrow &-18x & = &10\\\Leftrightarrow & \color{red}{-18}x & = &10\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{10}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{9} } & & \\ & V = \left\{ \frac{-5}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & -3x \color{red}{-7}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-7}\color{blue}{+7-x } & = & -7 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -7 \color{blue}{+7} \\\Leftrightarrow &-4x & = &0\\\Leftrightarrow & \color{red}{-4}x & = &0\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{0}{-4} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & 14x \color{red}{-7}& = & 15 \color{red}{ +3x } \\\Leftrightarrow & 14x \color{red}{-7}\color{blue}{+7-3x } & = & 15 \color{red}{ +3x }\color{blue}{+7-3x } \\\Leftrightarrow & 14x \color{blue}{-3x } & = & 15 \color{blue}{+7} \\\Leftrightarrow &11x & = &22\\\Leftrightarrow & \color{red}{11}x & = &22\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{22}{11} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
12. \(\begin{align} & -12x \color{red}{+1}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+1}\color{blue}{-1-x } & = & 12 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 12 \color{blue}{-1} \\\Leftrightarrow &-13x & = &11\\\Leftrightarrow & \color{red}{-13}x & = &11\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{11}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{13} } & & \\ & V = \left\{ \frac{-11}{13} \right\} & \\\end{align}\)