Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{-5}& = & -11 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{-5}\color{blue}{+5-x } & = & -11 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & -11 \color{blue}{+5} \\\Leftrightarrow &7x & = &-6\\\Leftrightarrow & \color{red}{7}x & = &-6\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-6}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{7} } & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{-12}& = & 6 \color{red}{ +7x } \\\Leftrightarrow & 8x \color{red}{-12}\color{blue}{+12-7x } & = & 6 \color{red}{ +7x }\color{blue}{+12-7x } \\\Leftrightarrow & 8x \color{blue}{-7x } & = & 6 \color{blue}{+12} \\\Leftrightarrow &x & = &18\\\Leftrightarrow & \color{red}{}x & = &18\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 18 \\\Leftrightarrow & \color{green}{ x = 18 } & & \\ & V = \left\{ 18 \right\} & \\\end{align}\)
3. \(\begin{align} & 3x \color{red}{+5}& = & 14 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{+5}\color{blue}{-5+5x } & = & 14 \color{red}{ -5x }\color{blue}{-5+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & 14 \color{blue}{-5} \\\Leftrightarrow &8x & = &9\\\Leftrightarrow & \color{red}{8}x & = &9\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{9}{8} \\\Leftrightarrow & \color{green}{ x = \frac{9}{8} } & & \\ & V = \left\{ \frac{9}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & -13x \color{red}{-4}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-4}\color{blue}{+4-x } & = & -4 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -4 \color{blue}{+4} \\\Leftrightarrow &-14x & = &0\\\Leftrightarrow & \color{red}{-14}x & = &0\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{0}{-14} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & 5x \color{red}{+15}& = & -11 \color{red}{ -7x } \\\Leftrightarrow & 5x \color{red}{+15}\color{blue}{-15+7x } & = & -11 \color{red}{ -7x }\color{blue}{-15+7x } \\\Leftrightarrow & 5x \color{blue}{+7x } & = & -11 \color{blue}{-15} \\\Leftrightarrow &12x & = &-26\\\Leftrightarrow & \color{red}{12}x & = &-26\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{-26}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{6} } & & \\ & V = \left\{ \frac{-13}{6} \right\} & \\\end{align}\)
6. \(\begin{align} & -9x \color{red}{+6}& = & -1 \color{red}{ +10x } \\\Leftrightarrow & -9x \color{red}{+6}\color{blue}{-6-10x } & = & -1 \color{red}{ +10x }\color{blue}{-6-10x } \\\Leftrightarrow & -9x \color{blue}{-10x } & = & -1 \color{blue}{-6} \\\Leftrightarrow &-19x & = &-7\\\Leftrightarrow & \color{red}{-19}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-7}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{7}{19} } & & \\ & V = \left\{ \frac{7}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{+14}& = & -8 \color{red}{ -6x } \\\Leftrightarrow & x \color{red}{+14}\color{blue}{-14+6x } & = & -8 \color{red}{ -6x }\color{blue}{-14+6x } \\\Leftrightarrow & x \color{blue}{+6x } & = & -8 \color{blue}{-14} \\\Leftrightarrow &7x & = &-22\\\Leftrightarrow & \color{red}{7}x & = &-22\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-22}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{7} } & & \\ & V = \left\{ \frac{-22}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 2x \color{red}{-3}& = & 13 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-3}\color{blue}{+3-x } & = & 13 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 13 \color{blue}{+3} \\\Leftrightarrow &x & = &16\\\Leftrightarrow & \color{red}{}x & = &16\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 16 \\\Leftrightarrow & \color{green}{ x = 16 } & & \\ & V = \left\{ 16 \right\} & \\\end{align}\)
9. \(\begin{align} & -x \color{red}{+6}& = & -12 \color{red}{ +10x } \\\Leftrightarrow & -x \color{red}{+6}\color{blue}{-6-10x } & = & -12 \color{red}{ +10x }\color{blue}{-6-10x } \\\Leftrightarrow & -x \color{blue}{-10x } & = & -12 \color{blue}{-6} \\\Leftrightarrow &-11x & = &-18\\\Leftrightarrow & \color{red}{-11}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-18}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{18}{11} } & & \\ & V = \left\{ \frac{18}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{+11}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+11}\color{blue}{-11-x } & = & 4 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 4 \color{blue}{-11} \\\Leftrightarrow &-6x & = &-7\\\Leftrightarrow & \color{red}{-6}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-7}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{7}{6} } & & \\ & V = \left\{ \frac{7}{6} \right\} & \\\end{align}\)
11. \(\begin{align} & x \color{red}{+1}& = & 5 \color{red}{ -15x } \\\Leftrightarrow & x \color{red}{+1}\color{blue}{-1+15x } & = & 5 \color{red}{ -15x }\color{blue}{-1+15x } \\\Leftrightarrow & x \color{blue}{+15x } & = & 5 \color{blue}{-1} \\\Leftrightarrow &16x & = &4\\\Leftrightarrow & \color{red}{16}x & = &4\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{4}{16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & -4x \color{red}{+12}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+12}\color{blue}{-12-x } & = & 8 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 8 \color{blue}{-12} \\\Leftrightarrow &-5x & = &-4\\\Leftrightarrow & \color{red}{-5}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-4}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)