Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -2x \color{red}{-15}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-15}\color{blue}{+15-x } & = & 12 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 12 \color{blue}{+15} \\\Leftrightarrow &-3x & = &27\\\Leftrightarrow & \color{red}{-3}x & = &27\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{27}{-3} \\\Leftrightarrow & \color{green}{ x = -9 } & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{-10}& = & -2 \color{red}{ +3x } \\\Leftrightarrow & -2x \color{red}{-10}\color{blue}{+10-3x } & = & -2 \color{red}{ +3x }\color{blue}{+10-3x } \\\Leftrightarrow & -2x \color{blue}{-3x } & = & -2 \color{blue}{+10} \\\Leftrightarrow &-5x & = &8\\\Leftrightarrow & \color{red}{-5}x & = &8\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{8}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{5} } & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -7x \color{red}{+4}& = & 1 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{+4}\color{blue}{-4-11x } & = & 1 \color{red}{ +11x }\color{blue}{-4-11x } \\\Leftrightarrow & -7x \color{blue}{-11x } & = & 1 \color{blue}{-4} \\\Leftrightarrow &-18x & = &-3\\\Leftrightarrow & \color{red}{-18}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{-3}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{1}{6} } & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)
4. \(\begin{align} & x \color{red}{+1}& = & 15 \color{red}{ -x } \\\Leftrightarrow & x \color{red}{+1}\color{blue}{-1+x } & = & 15 \color{red}{ -x }\color{blue}{-1+x } \\\Leftrightarrow & x \color{blue}{+x } & = & 15 \color{blue}{-1} \\\Leftrightarrow &2x & = &14\\\Leftrightarrow & \color{red}{2}x & = &14\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{14}{2} \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
5. \(\begin{align} & 2x \color{red}{-1}& = & 13 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-1}\color{blue}{+1-x } & = & 13 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 13 \color{blue}{+1} \\\Leftrightarrow &x & = &14\\\Leftrightarrow & \color{red}{}x & = &14\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 14 \\\Leftrightarrow & \color{green}{ x = 14 } & & \\ & V = \left\{ 14 \right\} & \\\end{align}\)
6. \(\begin{align} & 7x \color{red}{-6}& = & 11 \color{red}{ -9x } \\\Leftrightarrow & 7x \color{red}{-6}\color{blue}{+6+9x } & = & 11 \color{red}{ -9x }\color{blue}{+6+9x } \\\Leftrightarrow & 7x \color{blue}{+9x } & = & 11 \color{blue}{+6} \\\Leftrightarrow &16x & = &17\\\Leftrightarrow & \color{red}{16}x & = &17\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{17}{16} \\\Leftrightarrow & \color{green}{ x = \frac{17}{16} } & & \\ & V = \left\{ \frac{17}{16} \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{-14}& = & -4 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{-14}\color{blue}{+14-11x } & = & -4 \color{red}{ +11x }\color{blue}{+14-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & -4 \color{blue}{+14} \\\Leftrightarrow &-21x & = &10\\\Leftrightarrow & \color{red}{-21}x & = &10\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{10}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{21} } & & \\ & V = \left\{ \frac{-10}{21} \right\} & \\\end{align}\)
8. \(\begin{align} & -15x \color{red}{-5}& = & -12 \color{red}{ +4x } \\\Leftrightarrow & -15x \color{red}{-5}\color{blue}{+5-4x } & = & -12 \color{red}{ +4x }\color{blue}{+5-4x } \\\Leftrightarrow & -15x \color{blue}{-4x } & = & -12 \color{blue}{+5} \\\Leftrightarrow &-19x & = &-7\\\Leftrightarrow & \color{red}{-19}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-7}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{7}{19} } & & \\ & V = \left\{ \frac{7}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{-7}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-7}\color{blue}{+7-x } & = & 14 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 14 \color{blue}{+7} \\\Leftrightarrow &-12x & = &21\\\Leftrightarrow & \color{red}{-12}x & = &21\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{21}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{4} } & & \\ & V = \left\{ \frac{-7}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & 3x \color{red}{+13}& = & 8 \color{red}{ -11x } \\\Leftrightarrow & 3x \color{red}{+13}\color{blue}{-13+11x } & = & 8 \color{red}{ -11x }\color{blue}{-13+11x } \\\Leftrightarrow & 3x \color{blue}{+11x } & = & 8 \color{blue}{-13} \\\Leftrightarrow &14x & = &-5\\\Leftrightarrow & \color{red}{14}x & = &-5\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-5}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{14} } & & \\ & V = \left\{ \frac{-5}{14} \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{-12}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-12}\color{blue}{+12-x } & = & 12 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 12 \color{blue}{+12} \\\Leftrightarrow &-11x & = &24\\\Leftrightarrow & \color{red}{-11}x & = &24\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{24}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{11} } & & \\ & V = \left\{ \frac{-24}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & -6x \color{red}{-13}& = & 7 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-13}\color{blue}{+13-13x } & = & 7 \color{red}{ +13x }\color{blue}{+13-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 7 \color{blue}{+13} \\\Leftrightarrow &-19x & = &20\\\Leftrightarrow & \color{red}{-19}x & = &20\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{20}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{19} } & & \\ & V = \left\{ \frac{-20}{19} \right\} & \\\end{align}\)