Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -12x \color{red}{+15}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+15}\color{blue}{-15-x } & = & 3 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 3 \color{blue}{-15} \\\Leftrightarrow &-13x & = &-12\\\Leftrightarrow & \color{red}{-13}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-12}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{12}{13} } & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{-14}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-14}\color{blue}{+14-x } & = & -6 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -6 \color{blue}{+14} \\\Leftrightarrow &-14x & = &8\\\Leftrightarrow & \color{red}{-14}x & = &8\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{8}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{-8}& = & 2 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{-8}\color{blue}{+8-6x } & = & 2 \color{red}{ +6x }\color{blue}{+8-6x } \\\Leftrightarrow & -5x \color{blue}{-6x } & = & 2 \color{blue}{+8} \\\Leftrightarrow &-11x & = &10\\\Leftrightarrow & \color{red}{-11}x & = &10\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{10}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{11} } & & \\ & V = \left\{ \frac{-10}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & 12x \color{red}{+2}& = & -1 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+2}\color{blue}{-2+11x } & = & -1 \color{red}{ -11x }\color{blue}{-2+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -1 \color{blue}{-2} \\\Leftrightarrow &23x & = &-3\\\Leftrightarrow & \color{red}{23}x & = &-3\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-3}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{23} } & & \\ & V = \left\{ \frac{-3}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & -x \color{red}{-2}& = & -9 \color{red}{ -9x } \\\Leftrightarrow & -x \color{red}{-2}\color{blue}{+2+9x } & = & -9 \color{red}{ -9x }\color{blue}{+2+9x } \\\Leftrightarrow & -x \color{blue}{+9x } & = & -9 \color{blue}{+2} \\\Leftrightarrow &8x & = &-7\\\Leftrightarrow & \color{red}{8}x & = &-7\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-7}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{8} } & & \\ & V = \left\{ \frac{-7}{8} \right\} & \\\end{align}\)
6. \(\begin{align} & -x \color{red}{-4}& = & 1 \color{red}{ +2x } \\\Leftrightarrow & -x \color{red}{-4}\color{blue}{+4-2x } & = & 1 \color{red}{ +2x }\color{blue}{+4-2x } \\\Leftrightarrow & -x \color{blue}{-2x } & = & 1 \color{blue}{+4} \\\Leftrightarrow &-3x & = &5\\\Leftrightarrow & \color{red}{-3}x & = &5\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{5}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -13x \color{red}{-7}& = & -11 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-7}\color{blue}{+7-7x } & = & -11 \color{red}{ +7x }\color{blue}{+7-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -11 \color{blue}{+7} \\\Leftrightarrow &-20x & = &-4\\\Leftrightarrow & \color{red}{-20}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-4}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 3x \color{red}{-6}& = & -11 \color{red}{ +10x } \\\Leftrightarrow & 3x \color{red}{-6}\color{blue}{+6-10x } & = & -11 \color{red}{ +10x }\color{blue}{+6-10x } \\\Leftrightarrow & 3x \color{blue}{-10x } & = & -11 \color{blue}{+6} \\\Leftrightarrow &-7x & = &-5\\\Leftrightarrow & \color{red}{-7}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-5}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{5}{7} } & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & 14x \color{red}{+7}& = & -9 \color{red}{ +5x } \\\Leftrightarrow & 14x \color{red}{+7}\color{blue}{-7-5x } & = & -9 \color{red}{ +5x }\color{blue}{-7-5x } \\\Leftrightarrow & 14x \color{blue}{-5x } & = & -9 \color{blue}{-7} \\\Leftrightarrow &9x & = &-16\\\Leftrightarrow & \color{red}{9}x & = &-16\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-16}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{9} } & & \\ & V = \left\{ \frac{-16}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & 6x \color{red}{+15}& = & -13 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+15}\color{blue}{-15+11x } & = & -13 \color{red}{ -11x }\color{blue}{-15+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -13 \color{blue}{-15} \\\Leftrightarrow &17x & = &-28\\\Leftrightarrow & \color{red}{17}x & = &-28\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-28}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-28}{17} } & & \\ & V = \left\{ \frac{-28}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{-2}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-2}\color{blue}{+2-x } & = & -7 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -7 \color{blue}{+2} \\\Leftrightarrow &-7x & = &-5\\\Leftrightarrow & \color{red}{-7}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-5}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{5}{7} } & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{-12}& = & -13 \color{red}{ +14x } \\\Leftrightarrow & 13x \color{red}{-12}\color{blue}{+12-14x } & = & -13 \color{red}{ +14x }\color{blue}{+12-14x } \\\Leftrightarrow & 13x \color{blue}{-14x } & = & -13 \color{blue}{+12} \\\Leftrightarrow &-x & = &-1\\\Leftrightarrow & \color{red}{-}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-1}{-1} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)