Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

1. \(15x+3=-14-11x\)
2. \(15x+15=-15-2x\)
3. \(-8x+11=-13+9x\)
4. \(-15x-7=-11+x\)
5. \(3x-1=5-2x\)
6. \(-9x+4=10+x\)
7. \(-12x+2=13+x\)
8. \(8x+11=-11+x\)
9. \(-8x-6=8+x\)
10. \(-x+4=2+0x\)
11. \(-13x-15=-2+7x\)
12. \(2x+10=7+x\)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 15x \color{red}{+3}& = & -14 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{+3}\color{blue}{-3+11x } & = & -14 \color{red}{ -11x }\color{blue}{-3+11x } \\\Leftrightarrow & 15x \color{blue}{+11x } & = & -14 \color{blue}{-3} \\\Leftrightarrow &26x & = &-17\\\Leftrightarrow & \color{red}{26}x & = &-17\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}} & = & \frac{-17}{26} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{26} } & & \\ & V = \left\{ \frac{-17}{26} \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{+15}& = & -15 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{+15}\color{blue}{-15+2x } & = & -15 \color{red}{ -2x }\color{blue}{-15+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & -15 \color{blue}{-15} \\\Leftrightarrow &17x & = &-30\\\Leftrightarrow & \color{red}{17}x & = &-30\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-30}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-30}{17} } & & \\ & V = \left\{ \frac{-30}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & -8x \color{red}{+11}& = & -13 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+11}\color{blue}{-11-9x } & = & -13 \color{red}{ +9x }\color{blue}{-11-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & -13 \color{blue}{-11} \\\Leftrightarrow &-17x & = &-24\\\Leftrightarrow & \color{red}{-17}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-24}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{24}{17} } & & \\ & V = \left\{ \frac{24}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{-7}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-7}\color{blue}{+7-x } & = & -11 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -11 \color{blue}{+7} \\\Leftrightarrow &-16x & = &-4\\\Leftrightarrow & \color{red}{-16}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-4}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & 3x \color{red}{-1}& = & 5 \color{red}{ -2x } \\\Leftrightarrow & 3x \color{red}{-1}\color{blue}{+1+2x } & = & 5 \color{red}{ -2x }\color{blue}{+1+2x } \\\Leftrightarrow & 3x \color{blue}{+2x } & = & 5 \color{blue}{+1} \\\Leftrightarrow &5x & = &6\\\Leftrightarrow & \color{red}{5}x & = &6\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{6}{5} \\\Leftrightarrow & \color{green}{ x = \frac{6}{5} } & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -9x \color{red}{+4}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+4}\color{blue}{-4-x } & = & 10 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 10 \color{blue}{-4} \\\Leftrightarrow &-10x & = &6\\\Leftrightarrow & \color{red}{-10}x & = &6\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{6}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -12x \color{red}{+2}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+2}\color{blue}{-2-x } & = & 13 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 13 \color{blue}{-2} \\\Leftrightarrow &-13x & = &11\\\Leftrightarrow & \color{red}{-13}x & = &11\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{11}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{13} } & & \\ & V = \left\{ \frac{-11}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 8x \color{red}{+11}& = & -11 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+11}\color{blue}{-11-x } & = & -11 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & -11 \color{blue}{-11} \\\Leftrightarrow &7x & = &-22\\\Leftrightarrow & \color{red}{7}x & = &-22\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-22}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{7} } & & \\ & V = \left\{ \frac{-22}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -8x \color{red}{-6}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-6}\color{blue}{+6-x } & = & 8 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 8 \color{blue}{+6} \\\Leftrightarrow &-9x & = &14\\\Leftrightarrow & \color{red}{-9}x & = &14\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{14}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{9} } & & \\ & V = \left\{ \frac{-14}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{+4}& = & 2 \color{red}{ +0x } \\\Leftrightarrow & -x \color{red}{+4}\color{blue}{-4+0x } & = & 2 \color{red}{ +0x }\color{blue}{-4+0x } \\\Leftrightarrow & -x \color{blue}{+0x } & = & 2 \color{blue}{-4} \\\Leftrightarrow &-x & = &-2\\\Leftrightarrow & \color{red}{-}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-2}{-1} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
11. \(\begin{align} & -13x \color{red}{-15}& = & -2 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-15}\color{blue}{+15-7x } & = & -2 \color{red}{ +7x }\color{blue}{+15-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -2 \color{blue}{+15} \\\Leftrightarrow &-20x & = &13\\\Leftrightarrow & \color{red}{-20}x & = &13\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{13}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{20} } & & \\ & V = \left\{ \frac{-13}{20} \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{+10}& = & 7 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+10}\color{blue}{-10-x } & = & 7 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 7 \color{blue}{-10} \\\Leftrightarrow &x & = &-3\\\Leftrightarrow & \color{red}{}x & = &-3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -3 \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)