Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -x \color{red}{-7}& = & -12 \color{red}{ -12x } \\\Leftrightarrow & -x \color{red}{-7}\color{blue}{+7+12x } & = & -12 \color{red}{ -12x }\color{blue}{+7+12x } \\\Leftrightarrow & -x \color{blue}{+12x } & = & -12 \color{blue}{+7} \\\Leftrightarrow &11x & = &-5\\\Leftrightarrow & \color{red}{11}x & = &-5\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-5}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{11} } & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{-15}& = & 10 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{-15}\color{blue}{+15-8x } & = & 10 \color{red}{ +8x }\color{blue}{+15-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & 10 \color{blue}{+15} \\\Leftrightarrow &-23x & = &25\\\Leftrightarrow & \color{red}{-23}x & = &25\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{25}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{23} } & & \\ & V = \left\{ \frac{-25}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{-4}& = & -1 \color{red}{ +5x } \\\Leftrightarrow & -2x \color{red}{-4}\color{blue}{+4-5x } & = & -1 \color{red}{ +5x }\color{blue}{+4-5x } \\\Leftrightarrow & -2x \color{blue}{-5x } & = & -1 \color{blue}{+4} \\\Leftrightarrow &-7x & = &3\\\Leftrightarrow & \color{red}{-7}x & = &3\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{3}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 8x \color{red}{+11}& = & -1 \color{red}{ +7x } \\\Leftrightarrow & 8x \color{red}{+11}\color{blue}{-11-7x } & = & -1 \color{red}{ +7x }\color{blue}{-11-7x } \\\Leftrightarrow & 8x \color{blue}{-7x } & = & -1 \color{blue}{-11} \\\Leftrightarrow &x & = &-12\\\Leftrightarrow & \color{red}{}x & = &-12\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -12 \\\Leftrightarrow & \color{green}{ x = -12 } & & \\ & V = \left\{ -12 \right\} & \\\end{align}\)
5. \(\begin{align} & 7x \color{red}{-11}& = & 7 \color{red}{ -6x } \\\Leftrightarrow & 7x \color{red}{-11}\color{blue}{+11+6x } & = & 7 \color{red}{ -6x }\color{blue}{+11+6x } \\\Leftrightarrow & 7x \color{blue}{+6x } & = & 7 \color{blue}{+11} \\\Leftrightarrow &13x & = &18\\\Leftrightarrow & \color{red}{13}x & = &18\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{18}{13} \\\Leftrightarrow & \color{green}{ x = \frac{18}{13} } & & \\ & V = \left\{ \frac{18}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 13x \color{red}{+11}& = & 1 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+11}\color{blue}{-11+6x } & = & 1 \color{red}{ -6x }\color{blue}{-11+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & 1 \color{blue}{-11} \\\Leftrightarrow &19x & = &-10\\\Leftrightarrow & \color{red}{19}x & = &-10\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-10}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{19} } & & \\ & V = \left\{ \frac{-10}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{+5}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+5}\color{blue}{-5-x } & = & -2 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -2 \color{blue}{-5} \\\Leftrightarrow &-5x & = &-7\\\Leftrightarrow & \color{red}{-5}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-7}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 3x \color{red}{+12}& = & 15 \color{red}{ +8x } \\\Leftrightarrow & 3x \color{red}{+12}\color{blue}{-12-8x } & = & 15 \color{red}{ +8x }\color{blue}{-12-8x } \\\Leftrightarrow & 3x \color{blue}{-8x } & = & 15 \color{blue}{-12} \\\Leftrightarrow &-5x & = &3\\\Leftrightarrow & \color{red}{-5}x & = &3\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{3}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 10x \color{red}{-5}& = & 11 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{-5}\color{blue}{+5+13x } & = & 11 \color{red}{ -13x }\color{blue}{+5+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & 11 \color{blue}{+5} \\\Leftrightarrow &23x & = &16\\\Leftrightarrow & \color{red}{23}x & = &16\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{16}{23} \\\Leftrightarrow & \color{green}{ x = \frac{16}{23} } & & \\ & V = \left\{ \frac{16}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{-1}& = & 12 \color{red}{ +2x } \\\Leftrightarrow & 7x \color{red}{-1}\color{blue}{+1-2x } & = & 12 \color{red}{ +2x }\color{blue}{+1-2x } \\\Leftrightarrow & 7x \color{blue}{-2x } & = & 12 \color{blue}{+1} \\\Leftrightarrow &5x & = &13\\\Leftrightarrow & \color{red}{5}x & = &13\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{13}{5} \\\Leftrightarrow & \color{green}{ x = \frac{13}{5} } & & \\ & V = \left\{ \frac{13}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 15x \color{red}{-8}& = & -2 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{-8}\color{blue}{+8+7x } & = & -2 \color{red}{ -7x }\color{blue}{+8+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & -2 \color{blue}{+8} \\\Leftrightarrow &22x & = &6\\\Leftrightarrow & \color{red}{22}x & = &6\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{6}{22} \\\Leftrightarrow & \color{green}{ x = \frac{3}{11} } & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & -8x \color{red}{+6}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+6}\color{blue}{-6-x } & = & 4 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 4 \color{blue}{-6} \\\Leftrightarrow &-9x & = &-2\\\Leftrightarrow & \color{red}{-9}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-2}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{9} } & & \\ & V = \left\{ \frac{2}{9} \right\} & \\\end{align}\)