Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{+1}& = & -12 \color{red}{ -9x } \\\Leftrightarrow & 14x \color{red}{+1}\color{blue}{-1+9x } & = & -12 \color{red}{ -9x }\color{blue}{-1+9x } \\\Leftrightarrow & 14x \color{blue}{+9x } & = & -12 \color{blue}{-1} \\\Leftrightarrow &23x & = &-13\\\Leftrightarrow & \color{red}{23}x & = &-13\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-13}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{23} } & & \\ & V = \left\{ \frac{-13}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & 2x \color{red}{+6}& = & -7 \color{red}{ +7x } \\\Leftrightarrow & 2x \color{red}{+6}\color{blue}{-6-7x } & = & -7 \color{red}{ +7x }\color{blue}{-6-7x } \\\Leftrightarrow & 2x \color{blue}{-7x } & = & -7 \color{blue}{-6} \\\Leftrightarrow &-5x & = &-13\\\Leftrightarrow & \color{red}{-5}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-13}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{13}{5} } & & \\ & V = \left\{ \frac{13}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{-3}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-3}\color{blue}{+3-x } & = & -14 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -14 \color{blue}{+3} \\\Leftrightarrow &11x & = &-11\\\Leftrightarrow & \color{red}{11}x & = &-11\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-11}{11} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
4. \(\begin{align} & -9x \color{red}{-9}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-9}\color{blue}{+9-x } & = & 2 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 2 \color{blue}{+9} \\\Leftrightarrow &-10x & = &11\\\Leftrightarrow & \color{red}{-10}x & = &11\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{11}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{10} } & & \\ & V = \left\{ \frac{-11}{10} \right\} & \\\end{align}\)
5. \(\begin{align} & -15x \color{red}{+8}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+8}\color{blue}{-8-x } & = & -10 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -10 \color{blue}{-8} \\\Leftrightarrow &-16x & = &-18\\\Leftrightarrow & \color{red}{-16}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-18}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{9}{8} } & & \\ & V = \left\{ \frac{9}{8} \right\} & \\\end{align}\)
6. \(\begin{align} & x \color{red}{-13}& = & -10 \color{red}{ +11x } \\\Leftrightarrow & x \color{red}{-13}\color{blue}{+13-11x } & = & -10 \color{red}{ +11x }\color{blue}{+13-11x } \\\Leftrightarrow & x \color{blue}{-11x } & = & -10 \color{blue}{+13} \\\Leftrightarrow &-10x & = &3\\\Leftrightarrow & \color{red}{-10}x & = &3\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{3}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{10} } & & \\ & V = \left\{ \frac{-3}{10} \right\} & \\\end{align}\)
7. \(\begin{align} & 3x \color{red}{-13}& = & -6 \color{red}{ -11x } \\\Leftrightarrow & 3x \color{red}{-13}\color{blue}{+13+11x } & = & -6 \color{red}{ -11x }\color{blue}{+13+11x } \\\Leftrightarrow & 3x \color{blue}{+11x } & = & -6 \color{blue}{+13} \\\Leftrightarrow &14x & = &7\\\Leftrightarrow & \color{red}{14}x & = &7\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{7}{14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & 14x \color{red}{+14}& = & -15 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{+14}\color{blue}{-14+13x } & = & -15 \color{red}{ -13x }\color{blue}{-14+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & -15 \color{blue}{-14} \\\Leftrightarrow &27x & = &-29\\\Leftrightarrow & \color{red}{27}x & = &-29\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{-29}{27} \\\Leftrightarrow & \color{green}{ x = \frac{-29}{27} } & & \\ & V = \left\{ \frac{-29}{27} \right\} & \\\end{align}\)
9. \(\begin{align} & 8x \color{red}{+2}& = & 6 \color{red}{ +5x } \\\Leftrightarrow & 8x \color{red}{+2}\color{blue}{-2-5x } & = & 6 \color{red}{ +5x }\color{blue}{-2-5x } \\\Leftrightarrow & 8x \color{blue}{-5x } & = & 6 \color{blue}{-2} \\\Leftrightarrow &3x & = &4\\\Leftrightarrow & \color{red}{3}x & = &4\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{4}{3} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{+10}& = & -8 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+10}\color{blue}{-10+6x } & = & -8 \color{red}{ -6x }\color{blue}{-10+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -8 \color{blue}{-10} \\\Leftrightarrow &19x & = &-18\\\Leftrightarrow & \color{red}{19}x & = &-18\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-18}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{19} } & & \\ & V = \left\{ \frac{-18}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & -11x \color{red}{-4}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-4}\color{blue}{+4-x } & = & 1 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 1 \color{blue}{+4} \\\Leftrightarrow &-12x & = &5\\\Leftrightarrow & \color{red}{-12}x & = &5\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{5}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{12} } & & \\ & V = \left\{ \frac{-5}{12} \right\} & \\\end{align}\)
12. \(\begin{align} & 10x \color{red}{-8}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{-8}\color{blue}{+8-x } & = & -3 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & -3 \color{blue}{+8} \\\Leftrightarrow &9x & = &5\\\Leftrightarrow & \color{red}{9}x & = &5\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{5}{9} \\\Leftrightarrow & \color{green}{ x = \frac{5}{9} } & & \\ & V = \left\{ \frac{5}{9} \right\} & \\\end{align}\)