Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -11x \color{red}{-1}& = & -10 \color{red}{ +12x } \\\Leftrightarrow & -11x \color{red}{-1}\color{blue}{+1-12x } & = & -10 \color{red}{ +12x }\color{blue}{+1-12x } \\\Leftrightarrow & -11x \color{blue}{-12x } & = & -10 \color{blue}{+1} \\\Leftrightarrow &-23x & = &-9\\\Leftrightarrow & \color{red}{-23}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-9}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{9}{23} } & & \\ & V = \left\{ \frac{9}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & -9x \color{red}{+15}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+15}\color{blue}{-15-x } & = & 13 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 13 \color{blue}{-15} \\\Leftrightarrow &-10x & = &-2\\\Leftrightarrow & \color{red}{-10}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-2}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -6x \color{red}{-4}& = & 5 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-4}\color{blue}{+4-13x } & = & 5 \color{red}{ +13x }\color{blue}{+4-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 5 \color{blue}{+4} \\\Leftrightarrow &-19x & = &9\\\Leftrightarrow & \color{red}{-19}x & = &9\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{9}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{19} } & & \\ & V = \left\{ \frac{-9}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & 14x \color{red}{+1}& = & -15 \color{red}{ -11x } \\\Leftrightarrow & 14x \color{red}{+1}\color{blue}{-1+11x } & = & -15 \color{red}{ -11x }\color{blue}{-1+11x } \\\Leftrightarrow & 14x \color{blue}{+11x } & = & -15 \color{blue}{-1} \\\Leftrightarrow &25x & = &-16\\\Leftrightarrow & \color{red}{25}x & = &-16\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{-16}{25} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{25} } & & \\ & V = \left\{ \frac{-16}{25} \right\} & \\\end{align}\)
5. \(\begin{align} & -4x \color{red}{+4}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+4}\color{blue}{-4-x } & = & -14 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -14 \color{blue}{-4} \\\Leftrightarrow &-5x & = &-18\\\Leftrightarrow & \color{red}{-5}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-18}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{18}{5} } & & \\ & V = \left\{ \frac{18}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -7x \color{red}{+4}& = & -14 \color{red}{ +8x } \\\Leftrightarrow & -7x \color{red}{+4}\color{blue}{-4-8x } & = & -14 \color{red}{ +8x }\color{blue}{-4-8x } \\\Leftrightarrow & -7x \color{blue}{-8x } & = & -14 \color{blue}{-4} \\\Leftrightarrow &-15x & = &-18\\\Leftrightarrow & \color{red}{-15}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-18}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{6}{5} } & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 7x \color{red}{-2}& = & 4 \color{red}{ +x } \\\Leftrightarrow & 7x \color{red}{-2}\color{blue}{+2-x } & = & 4 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & 7x \color{blue}{-x } & = & 4 \color{blue}{+2} \\\Leftrightarrow &6x & = &6\\\Leftrightarrow & \color{red}{6}x & = &6\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{6}{6} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
8. \(\begin{align} & -13x \color{red}{+9}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+9}\color{blue}{-9-x } & = & -6 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -6 \color{blue}{-9} \\\Leftrightarrow &-14x & = &-15\\\Leftrightarrow & \color{red}{-14}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-15}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{15}{14} } & & \\ & V = \left\{ \frac{15}{14} \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{+6}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+6}\color{blue}{-6-x } & = & 4 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 4 \color{blue}{-6} \\\Leftrightarrow &-7x & = &-2\\\Leftrightarrow & \color{red}{-7}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-2}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 11x \color{red}{+2}& = & -7 \color{red}{ +4x } \\\Leftrightarrow & 11x \color{red}{+2}\color{blue}{-2-4x } & = & -7 \color{red}{ +4x }\color{blue}{-2-4x } \\\Leftrightarrow & 11x \color{blue}{-4x } & = & -7 \color{blue}{-2} \\\Leftrightarrow &7x & = &-9\\\Leftrightarrow & \color{red}{7}x & = &-9\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-9}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & 3x \color{red}{-3}& = & -10 \color{red}{ +13x } \\\Leftrightarrow & 3x \color{red}{-3}\color{blue}{+3-13x } & = & -10 \color{red}{ +13x }\color{blue}{+3-13x } \\\Leftrightarrow & 3x \color{blue}{-13x } & = & -10 \color{blue}{+3} \\\Leftrightarrow &-10x & = &-7\\\Leftrightarrow & \color{red}{-10}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-7}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{7}{10} } & & \\ & V = \left\{ \frac{7}{10} \right\} & \\\end{align}\)
12. \(\begin{align} & -6x \color{red}{+10}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+10}\color{blue}{-10-x } & = & -13 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -13 \color{blue}{-10} \\\Leftrightarrow &-7x & = &-23\\\Leftrightarrow & \color{red}{-7}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-23}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{23}{7} } & & \\ & V = \left\{ \frac{23}{7} \right\} & \\\end{align}\)