Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -11x \color{red}{+3}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+3}\color{blue}{-3-x } & = & -14 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -14 \color{blue}{-3} \\\Leftrightarrow &-12x & = &-17\\\Leftrightarrow & \color{red}{-12}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-17}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{17}{12} } & & \\ & V = \left\{ \frac{17}{12} \right\} & \\\end{align}\)
2. \(\begin{align} & 3x \color{red}{-13}& = & 14 \color{red}{ +x } \\\Leftrightarrow & 3x \color{red}{-13}\color{blue}{+13-x } & = & 14 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & 3x \color{blue}{-x } & = & 14 \color{blue}{+13} \\\Leftrightarrow &2x & = &27\\\Leftrightarrow & \color{red}{2}x & = &27\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{27}{2} \\\Leftrightarrow & \color{green}{ x = \frac{27}{2} } & & \\ & V = \left\{ \frac{27}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & -10x \color{red}{+8}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+8}\color{blue}{-8-x } & = & -3 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -3 \color{blue}{-8} \\\Leftrightarrow &-11x & = &-11\\\Leftrightarrow & \color{red}{-11}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-11}{-11} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
4. \(\begin{align} & -x \color{red}{+7}& = & 11 \color{red}{ +3x } \\\Leftrightarrow & -x \color{red}{+7}\color{blue}{-7-3x } & = & 11 \color{red}{ +3x }\color{blue}{-7-3x } \\\Leftrightarrow & -x \color{blue}{-3x } & = & 11 \color{blue}{-7} \\\Leftrightarrow &-4x & = &4\\\Leftrightarrow & \color{red}{-4}x & = &4\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{4}{-4} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
5. \(\begin{align} & -2x \color{red}{-9}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-9}\color{blue}{+9-x } & = & 5 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 5 \color{blue}{+9} \\\Leftrightarrow &-3x & = &14\\\Leftrightarrow & \color{red}{-3}x & = &14\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{14}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{3} } & & \\ & V = \left\{ \frac{-14}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & 11x \color{red}{-12}& = & -4 \color{red}{ -5x } \\\Leftrightarrow & 11x \color{red}{-12}\color{blue}{+12+5x } & = & -4 \color{red}{ -5x }\color{blue}{+12+5x } \\\Leftrightarrow & 11x \color{blue}{+5x } & = & -4 \color{blue}{+12} \\\Leftrightarrow &16x & = &8\\\Leftrightarrow & \color{red}{16}x & = &8\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{8}{16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{-4}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-4}\color{blue}{+4-x } & = & 4 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 4 \color{blue}{+4} \\\Leftrightarrow &-11x & = &8\\\Leftrightarrow & \color{red}{-11}x & = &8\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{8}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{11} } & & \\ & V = \left\{ \frac{-8}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{+9}& = & 5 \color{red}{ +10x } \\\Leftrightarrow & 9x \color{red}{+9}\color{blue}{-9-10x } & = & 5 \color{red}{ +10x }\color{blue}{-9-10x } \\\Leftrightarrow & 9x \color{blue}{-10x } & = & 5 \color{blue}{-9} \\\Leftrightarrow &-x & = &-4\\\Leftrightarrow & \color{red}{-}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-4}{-1} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
9. \(\begin{align} & 14x \color{red}{-4}& = & 7 \color{red}{ +13x } \\\Leftrightarrow & 14x \color{red}{-4}\color{blue}{+4-13x } & = & 7 \color{red}{ +13x }\color{blue}{+4-13x } \\\Leftrightarrow & 14x \color{blue}{-13x } & = & 7 \color{blue}{+4} \\\Leftrightarrow &x & = &11\\\Leftrightarrow & \color{red}{}x & = &11\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 11 \\\Leftrightarrow & \color{green}{ x = 11 } & & \\ & V = \left\{ 11 \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{+15}& = & -15 \color{red}{ -3x } \\\Leftrightarrow & 13x \color{red}{+15}\color{blue}{-15+3x } & = & -15 \color{red}{ -3x }\color{blue}{-15+3x } \\\Leftrightarrow & 13x \color{blue}{+3x } & = & -15 \color{blue}{-15} \\\Leftrightarrow &16x & = &-30\\\Leftrightarrow & \color{red}{16}x & = &-30\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{-30}{16} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{8} } & & \\ & V = \left\{ \frac{-15}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{-14}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-14}\color{blue}{+14-x } & = & 15 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 15 \color{blue}{+14} \\\Leftrightarrow &-7x & = &29\\\Leftrightarrow & \color{red}{-7}x & = &29\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{29}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-29}{7} } & & \\ & V = \left\{ \frac{-29}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -5x \color{red}{-8}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-8}\color{blue}{+8-x } & = & 5 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 5 \color{blue}{+8} \\\Leftrightarrow &-6x & = &13\\\Leftrightarrow & \color{red}{-6}x & = &13\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{13}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{6} } & & \\ & V = \left\{ \frac{-13}{6} \right\} & \\\end{align}\)