Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{+5}& = & -11 \color{red}{ -9x } \\\Leftrightarrow & 14x \color{red}{+5}\color{blue}{-5+9x } & = & -11 \color{red}{ -9x }\color{blue}{-5+9x } \\\Leftrightarrow & 14x \color{blue}{+9x } & = & -11 \color{blue}{-5} \\\Leftrightarrow &23x & = &-16\\\Leftrightarrow & \color{red}{23}x & = &-16\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-16}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{23} } & & \\ & V = \left\{ \frac{-16}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{+12}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+12}\color{blue}{-12-x } & = & 8 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 8 \color{blue}{-12} \\\Leftrightarrow &-9x & = &-4\\\Leftrightarrow & \color{red}{-9}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-4}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{4}{9} } & & \\ & V = \left\{ \frac{4}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & -6x \color{red}{+10}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+10}\color{blue}{-10-x } & = & 12 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 12 \color{blue}{-10} \\\Leftrightarrow &-7x & = &2\\\Leftrightarrow & \color{red}{-7}x & = &2\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{2}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & -5x \color{red}{+2}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+2}\color{blue}{-2-x } & = & -4 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -4 \color{blue}{-2} \\\Leftrightarrow &-6x & = &-6\\\Leftrightarrow & \color{red}{-6}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-6}{-6} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{+6}& = & 7 \color{red}{ -2x } \\\Leftrightarrow & 9x \color{red}{+6}\color{blue}{-6+2x } & = & 7 \color{red}{ -2x }\color{blue}{-6+2x } \\\Leftrightarrow & 9x \color{blue}{+2x } & = & 7 \color{blue}{-6} \\\Leftrightarrow &11x & = &1\\\Leftrightarrow & \color{red}{11}x & = &1\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{1}{11} \\\Leftrightarrow & \color{green}{ x = \frac{1}{11} } & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & x \color{red}{+3}& = & 13 \color{red}{ +5x } \\\Leftrightarrow & x \color{red}{+3}\color{blue}{-3-5x } & = & 13 \color{red}{ +5x }\color{blue}{-3-5x } \\\Leftrightarrow & x \color{blue}{-5x } & = & 13 \color{blue}{-3} \\\Leftrightarrow &-4x & = &10\\\Leftrightarrow & \color{red}{-4}x & = &10\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{10}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & -7x \color{red}{+15}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+15}\color{blue}{-15-x } & = & -8 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -8 \color{blue}{-15} \\\Leftrightarrow &-8x & = &-23\\\Leftrightarrow & \color{red}{-8}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-23}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{23}{8} } & & \\ & V = \left\{ \frac{23}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & -5x \color{red}{+15}& = & 4 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{+15}\color{blue}{-15-11x } & = & 4 \color{red}{ +11x }\color{blue}{-15-11x } \\\Leftrightarrow & -5x \color{blue}{-11x } & = & 4 \color{blue}{-15} \\\Leftrightarrow &-16x & = &-11\\\Leftrightarrow & \color{red}{-16}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-11}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{11}{16} } & & \\ & V = \left\{ \frac{11}{16} \right\} & \\\end{align}\)
9. \(\begin{align} & -8x \color{red}{-3}& = & 1 \color{red}{ +11x } \\\Leftrightarrow & -8x \color{red}{-3}\color{blue}{+3-11x } & = & 1 \color{red}{ +11x }\color{blue}{+3-11x } \\\Leftrightarrow & -8x \color{blue}{-11x } & = & 1 \color{blue}{+3} \\\Leftrightarrow &-19x & = &4\\\Leftrightarrow & \color{red}{-19}x & = &4\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{4}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{19} } & & \\ & V = \left\{ \frac{-4}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{-6}& = & 12 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-6}\color{blue}{+6-7x } & = & 12 \color{red}{ +7x }\color{blue}{+6-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & 12 \color{blue}{+6} \\\Leftrightarrow &-13x & = &18\\\Leftrightarrow & \color{red}{-13}x & = &18\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{18}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{13} } & & \\ & V = \left\{ \frac{-18}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & -11x \color{red}{+12}& = & 12 \color{red}{ +12x } \\\Leftrightarrow & -11x \color{red}{+12}\color{blue}{-12-12x } & = & 12 \color{red}{ +12x }\color{blue}{-12-12x } \\\Leftrightarrow & -11x \color{blue}{-12x } & = & 12 \color{blue}{-12} \\\Leftrightarrow &-23x & = &0\\\Leftrightarrow & \color{red}{-23}x & = &0\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{0}{-23} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{+1}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+1}\color{blue}{-1-x } & = & -5 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -5 \color{blue}{-1} \\\Leftrightarrow &-10x & = &-6\\\Leftrightarrow & \color{red}{-10}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-6}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)