Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -11x \color{red}{-8}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-8}\color{blue}{+8-x } & = & -12 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -12 \color{blue}{+8} \\\Leftrightarrow &-12x & = &-4\\\Leftrightarrow & \color{red}{-12}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-4}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & x \color{red}{+7}& = & -10 \color{red}{ +3x } \\\Leftrightarrow & x \color{red}{+7}\color{blue}{-7-3x } & = & -10 \color{red}{ +3x }\color{blue}{-7-3x } \\\Leftrightarrow & x \color{blue}{-3x } & = & -10 \color{blue}{-7} \\\Leftrightarrow &-2x & = &-17\\\Leftrightarrow & \color{red}{-2}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{-17}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{17}{2} } & & \\ & V = \left\{ \frac{17}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & 6x \color{red}{-5}& = & 12 \color{red}{ +7x } \\\Leftrightarrow & 6x \color{red}{-5}\color{blue}{+5-7x } & = & 12 \color{red}{ +7x }\color{blue}{+5-7x } \\\Leftrightarrow & 6x \color{blue}{-7x } & = & 12 \color{blue}{+5} \\\Leftrightarrow &-x & = &17\\\Leftrightarrow & \color{red}{-}x & = &17\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{17}{-1} \\\Leftrightarrow & \color{green}{ x = -17 } & & \\ & V = \left\{ -17 \right\} & \\\end{align}\)
4. \(\begin{align} & -8x \color{red}{+12}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+12}\color{blue}{-12-x } & = & 13 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 13 \color{blue}{-12} \\\Leftrightarrow &-9x & = &1\\\Leftrightarrow & \color{red}{-9}x & = &1\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{1}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{9} } & & \\ & V = \left\{ \frac{-1}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{+6}& = & -7 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+6}\color{blue}{-6-9x } & = & -7 \color{red}{ +9x }\color{blue}{-6-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & -7 \color{blue}{-6} \\\Leftrightarrow &-17x & = &-13\\\Leftrightarrow & \color{red}{-17}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-13}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{13}{17} } & & \\ & V = \left\{ \frac{13}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & -x \color{red}{+9}& = & -6 \color{red}{ -7x } \\\Leftrightarrow & -x \color{red}{+9}\color{blue}{-9+7x } & = & -6 \color{red}{ -7x }\color{blue}{-9+7x } \\\Leftrightarrow & -x \color{blue}{+7x } & = & -6 \color{blue}{-9} \\\Leftrightarrow &6x & = &-15\\\Leftrightarrow & \color{red}{6}x & = &-15\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{-15}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & 6x \color{red}{-1}& = & 13 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{-1}\color{blue}{+1-5x } & = & 13 \color{red}{ +5x }\color{blue}{+1-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & 13 \color{blue}{+1} \\\Leftrightarrow &x & = &14\\\Leftrightarrow & \color{red}{}x & = &14\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 14 \\\Leftrightarrow & \color{green}{ x = 14 } & & \\ & V = \left\{ 14 \right\} & \\\end{align}\)
8. \(\begin{align} & 8x \color{red}{-15}& = & -7 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{-15}\color{blue}{+15-x } & = & -7 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & -7 \color{blue}{+15} \\\Leftrightarrow &7x & = &8\\\Leftrightarrow & \color{red}{7}x & = &8\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{8}{7} \\\Leftrightarrow & \color{green}{ x = \frac{8}{7} } & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & 8x \color{red}{-4}& = & -9 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{-4}\color{blue}{+4+7x } & = & -9 \color{red}{ -7x }\color{blue}{+4+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & -9 \color{blue}{+4} \\\Leftrightarrow &15x & = &-5\\\Leftrightarrow & \color{red}{15}x & = &-5\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-5}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{-9}& = & 14 \color{red}{ +11x } \\\Leftrightarrow & 14x \color{red}{-9}\color{blue}{+9-11x } & = & 14 \color{red}{ +11x }\color{blue}{+9-11x } \\\Leftrightarrow & 14x \color{blue}{-11x } & = & 14 \color{blue}{+9} \\\Leftrightarrow &3x & = &23\\\Leftrightarrow & \color{red}{3}x & = &23\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{23}{3} \\\Leftrightarrow & \color{green}{ x = \frac{23}{3} } & & \\ & V = \left\{ \frac{23}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -7x \color{red}{+14}& = & -13 \color{red}{ +5x } \\\Leftrightarrow & -7x \color{red}{+14}\color{blue}{-14-5x } & = & -13 \color{red}{ +5x }\color{blue}{-14-5x } \\\Leftrightarrow & -7x \color{blue}{-5x } & = & -13 \color{blue}{-14} \\\Leftrightarrow &-12x & = &-27\\\Leftrightarrow & \color{red}{-12}x & = &-27\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-27}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{9}{4} } & & \\ & V = \left\{ \frac{9}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{+9}& = & -10 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{+9}\color{blue}{-9-5x } & = & -10 \color{red}{ +5x }\color{blue}{-9-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & -10 \color{blue}{-9} \\\Leftrightarrow &-14x & = &-19\\\Leftrightarrow & \color{red}{-14}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-19}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{19}{14} } & & \\ & V = \left\{ \frac{19}{14} \right\} & \\\end{align}\)