Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -12x \color{red}{+1}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+1}\color{blue}{-1-x } & = & -12 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -12 \color{blue}{-1} \\\Leftrightarrow &-13x & = &-13\\\Leftrightarrow & \color{red}{-13}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-13}{-13} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
2. \(\begin{align} & 7x \color{red}{+10}& = & -13 \color{red}{ -6x } \\\Leftrightarrow & 7x \color{red}{+10}\color{blue}{-10+6x } & = & -13 \color{red}{ -6x }\color{blue}{-10+6x } \\\Leftrightarrow & 7x \color{blue}{+6x } & = & -13 \color{blue}{-10} \\\Leftrightarrow &13x & = &-23\\\Leftrightarrow & \color{red}{13}x & = &-23\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-23}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{13} } & & \\ & V = \left\{ \frac{-23}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & 7x \color{red}{-1}& = & -6 \color{red}{ +9x } \\\Leftrightarrow & 7x \color{red}{-1}\color{blue}{+1-9x } & = & -6 \color{red}{ +9x }\color{blue}{+1-9x } \\\Leftrightarrow & 7x \color{blue}{-9x } & = & -6 \color{blue}{+1} \\\Leftrightarrow &-2x & = &-5\\\Leftrightarrow & \color{red}{-2}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{-5}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & 3x \color{red}{-12}& = & 11 \color{red}{ +8x } \\\Leftrightarrow & 3x \color{red}{-12}\color{blue}{+12-8x } & = & 11 \color{red}{ +8x }\color{blue}{+12-8x } \\\Leftrightarrow & 3x \color{blue}{-8x } & = & 11 \color{blue}{+12} \\\Leftrightarrow &-5x & = &23\\\Leftrightarrow & \color{red}{-5}x & = &23\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{23}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{5} } & & \\ & V = \left\{ \frac{-23}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -12x \color{red}{+14}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+14}\color{blue}{-14-x } & = & 7 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 7 \color{blue}{-14} \\\Leftrightarrow &-13x & = &-7\\\Leftrightarrow & \color{red}{-13}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-7}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{7}{13} } & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 5x \color{red}{-4}& = & 1 \color{red}{ -9x } \\\Leftrightarrow & 5x \color{red}{-4}\color{blue}{+4+9x } & = & 1 \color{red}{ -9x }\color{blue}{+4+9x } \\\Leftrightarrow & 5x \color{blue}{+9x } & = & 1 \color{blue}{+4} \\\Leftrightarrow &14x & = &5\\\Leftrightarrow & \color{red}{14}x & = &5\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{5}{14} \\\Leftrightarrow & \color{green}{ x = \frac{5}{14} } & & \\ & V = \left\{ \frac{5}{14} \right\} & \\\end{align}\)
7. \(\begin{align} & 14x \color{red}{-11}& = & -15 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-11}\color{blue}{+11-x } & = & -15 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -15 \color{blue}{+11} \\\Leftrightarrow &13x & = &-4\\\Leftrightarrow & \color{red}{13}x & = &-4\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-4}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{13} } & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & -6x \color{red}{+8}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+8}\color{blue}{-8-x } & = & -1 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -1 \color{blue}{-8} \\\Leftrightarrow &-7x & = &-9\\\Leftrightarrow & \color{red}{-7}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-9}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{9}{7} } & & \\ & V = \left\{ \frac{9}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & 14x \color{red}{+2}& = & 8 \color{red}{ +5x } \\\Leftrightarrow & 14x \color{red}{+2}\color{blue}{-2-5x } & = & 8 \color{red}{ +5x }\color{blue}{-2-5x } \\\Leftrightarrow & 14x \color{blue}{-5x } & = & 8 \color{blue}{-2} \\\Leftrightarrow &9x & = &6\\\Leftrightarrow & \color{red}{9}x & = &6\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{6}{9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{-10}& = & 11 \color{red}{ -14x } \\\Leftrightarrow & 5x \color{red}{-10}\color{blue}{+10+14x } & = & 11 \color{red}{ -14x }\color{blue}{+10+14x } \\\Leftrightarrow & 5x \color{blue}{+14x } & = & 11 \color{blue}{+10} \\\Leftrightarrow &19x & = &21\\\Leftrightarrow & \color{red}{19}x & = &21\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{21}{19} \\\Leftrightarrow & \color{green}{ x = \frac{21}{19} } & & \\ & V = \left\{ \frac{21}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & 8x \color{red}{+15}& = & -12 \color{red}{ +9x } \\\Leftrightarrow & 8x \color{red}{+15}\color{blue}{-15-9x } & = & -12 \color{red}{ +9x }\color{blue}{-15-9x } \\\Leftrightarrow & 8x \color{blue}{-9x } & = & -12 \color{blue}{-15} \\\Leftrightarrow &-x & = &-27\\\Leftrightarrow & \color{red}{-}x & = &-27\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-27}{-1} \\\Leftrightarrow & \color{green}{ x = 27 } & & \\ & V = \left\{ 27 \right\} & \\\end{align}\)
12. \(\begin{align} & -12x \color{red}{-6}& = & 5 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-6}\color{blue}{+6-13x } & = & 5 \color{red}{ +13x }\color{blue}{+6-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 5 \color{blue}{+6} \\\Leftrightarrow &-25x & = &11\\\Leftrightarrow & \color{red}{-25}x & = &11\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{11}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{25} } & & \\ & V = \left\{ \frac{-11}{25} \right\} & \\\end{align}\)