Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 10x \color{red}{-8}& = & -15 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{-8}\color{blue}{+8+9x } & = & -15 \color{red}{ -9x }\color{blue}{+8+9x } \\\Leftrightarrow & 10x \color{blue}{+9x } & = & -15 \color{blue}{+8} \\\Leftrightarrow &19x & = &-7\\\Leftrightarrow & \color{red}{19}x & = &-7\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-7}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{19} } & & \\ & V = \left\{ \frac{-7}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{-2}& = & -5 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{-2}\color{blue}{+2-7x } & = & -5 \color{red}{ +7x }\color{blue}{+2-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & -5 \color{blue}{+2} \\\Leftrightarrow &-17x & = &-3\\\Leftrightarrow & \color{red}{-17}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-3}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{3}{17} } & & \\ & V = \left\{ \frac{3}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{+1}& = & -1 \color{red}{ +2x } \\\Leftrightarrow & 11x \color{red}{+1}\color{blue}{-1-2x } & = & -1 \color{red}{ +2x }\color{blue}{-1-2x } \\\Leftrightarrow & 11x \color{blue}{-2x } & = & -1 \color{blue}{-1} \\\Leftrightarrow &9x & = &-2\\\Leftrightarrow & \color{red}{9}x & = &-2\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-2}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{9} } & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{-6}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-6}\color{blue}{+6-x } & = & 9 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 9 \color{blue}{+6} \\\Leftrightarrow &-12x & = &15\\\Leftrightarrow & \color{red}{-12}x & = &15\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{15}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & x \color{red}{+4}& = & 12 \color{red}{ +7x } \\\Leftrightarrow & x \color{red}{+4}\color{blue}{-4-7x } & = & 12 \color{red}{ +7x }\color{blue}{-4-7x } \\\Leftrightarrow & x \color{blue}{-7x } & = & 12 \color{blue}{-4} \\\Leftrightarrow &-6x & = &8\\\Leftrightarrow & \color{red}{-6}x & = &8\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{8}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -3x \color{red}{-4}& = & 12 \color{red}{ +10x } \\\Leftrightarrow & -3x \color{red}{-4}\color{blue}{+4-10x } & = & 12 \color{red}{ +10x }\color{blue}{+4-10x } \\\Leftrightarrow & -3x \color{blue}{-10x } & = & 12 \color{blue}{+4} \\\Leftrightarrow &-13x & = &16\\\Leftrightarrow & \color{red}{-13}x & = &16\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{16}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{13} } & & \\ & V = \left\{ \frac{-16}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 6x \color{red}{-2}& = & 15 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{-2}\color{blue}{+2+5x } & = & 15 \color{red}{ -5x }\color{blue}{+2+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & 15 \color{blue}{+2} \\\Leftrightarrow &11x & = &17\\\Leftrightarrow & \color{red}{11}x & = &17\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{17}{11} \\\Leftrightarrow & \color{green}{ x = \frac{17}{11} } & & \\ & V = \left\{ \frac{17}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 12x \color{red}{+2}& = & 3 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+2}\color{blue}{-2+11x } & = & 3 \color{red}{ -11x }\color{blue}{-2+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 3 \color{blue}{-2} \\\Leftrightarrow &23x & = &1\\\Leftrightarrow & \color{red}{23}x & = &1\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{1}{23} \\\Leftrightarrow & \color{green}{ x = \frac{1}{23} } & & \\ & V = \left\{ \frac{1}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{-7}& = & -3 \color{red}{ +3x } \\\Leftrightarrow & 13x \color{red}{-7}\color{blue}{+7-3x } & = & -3 \color{red}{ +3x }\color{blue}{+7-3x } \\\Leftrightarrow & 13x \color{blue}{-3x } & = & -3 \color{blue}{+7} \\\Leftrightarrow &10x & = &4\\\Leftrightarrow & \color{red}{10}x & = &4\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{4}{10} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -11x \color{red}{+8}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+8}\color{blue}{-8-x } & = & 3 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 3 \color{blue}{-8} \\\Leftrightarrow &-12x & = &-5\\\Leftrightarrow & \color{red}{-12}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-5}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{12} } & & \\ & V = \left\{ \frac{5}{12} \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{-4}& = & -5 \color{red}{ +4x } \\\Leftrightarrow & -3x \color{red}{-4}\color{blue}{+4-4x } & = & -5 \color{red}{ +4x }\color{blue}{+4-4x } \\\Leftrightarrow & -3x \color{blue}{-4x } & = & -5 \color{blue}{+4} \\\Leftrightarrow &-7x & = &-1\\\Leftrightarrow & \color{red}{-7}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-1}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -2x \color{red}{-3}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-3}\color{blue}{+3-x } & = & -6 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -6 \color{blue}{+3} \\\Leftrightarrow &-3x & = &-3\\\Leftrightarrow & \color{red}{-3}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-3}{-3} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)