Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{+1}& = & 14 \color{red}{ -5x } \\\Leftrightarrow & 8x \color{red}{+1}\color{blue}{-1+5x } & = & 14 \color{red}{ -5x }\color{blue}{-1+5x } \\\Leftrightarrow & 8x \color{blue}{+5x } & = & 14 \color{blue}{-1} \\\Leftrightarrow &13x & = &13\\\Leftrightarrow & \color{red}{13}x & = &13\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{13}{13} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{-15}& = & 8 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{-15}\color{blue}{+15-14x } & = & 8 \color{red}{ +14x }\color{blue}{+15-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & 8 \color{blue}{+15} \\\Leftrightarrow &-27x & = &23\\\Leftrightarrow & \color{red}{-27}x & = &23\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{23}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{27} } & & \\ & V = \left\{ \frac{-23}{27} \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{+3}& = & -14 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{+3}\color{blue}{-3-14x } & = & -14 \color{red}{ +14x }\color{blue}{-3-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & -14 \color{blue}{-3} \\\Leftrightarrow &-27x & = &-17\\\Leftrightarrow & \color{red}{-27}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{-17}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{17}{27} } & & \\ & V = \left\{ \frac{17}{27} \right\} & \\\end{align}\)
4. \(\begin{align} & -13x \color{red}{-14}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-14}\color{blue}{+14-x } & = & -5 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -5 \color{blue}{+14} \\\Leftrightarrow &-14x & = &9\\\Leftrightarrow & \color{red}{-14}x & = &9\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{9}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{14} } & & \\ & V = \left\{ \frac{-9}{14} \right\} & \\\end{align}\)
5. \(\begin{align} & 5x \color{red}{-6}& = & -1 \color{red}{ +8x } \\\Leftrightarrow & 5x \color{red}{-6}\color{blue}{+6-8x } & = & -1 \color{red}{ +8x }\color{blue}{+6-8x } \\\Leftrightarrow & 5x \color{blue}{-8x } & = & -1 \color{blue}{+6} \\\Leftrightarrow &-3x & = &5\\\Leftrightarrow & \color{red}{-3}x & = &5\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{5}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & 7x \color{red}{+5}& = & -11 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{+5}\color{blue}{-5+13x } & = & -11 \color{red}{ -13x }\color{blue}{-5+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & -11 \color{blue}{-5} \\\Leftrightarrow &20x & = &-16\\\Leftrightarrow & \color{red}{20}x & = &-16\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{-16}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -11x \color{red}{+1}& = & -2 \color{red}{ +9x } \\\Leftrightarrow & -11x \color{red}{+1}\color{blue}{-1-9x } & = & -2 \color{red}{ +9x }\color{blue}{-1-9x } \\\Leftrightarrow & -11x \color{blue}{-9x } & = & -2 \color{blue}{-1} \\\Leftrightarrow &-20x & = &-3\\\Leftrightarrow & \color{red}{-20}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-3}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{3}{20} } & & \\ & V = \left\{ \frac{3}{20} \right\} & \\\end{align}\)
8. \(\begin{align} & -15x \color{red}{+6}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+6}\color{blue}{-6-x } & = & -9 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -9 \color{blue}{-6} \\\Leftrightarrow &-16x & = &-15\\\Leftrightarrow & \color{red}{-16}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-15}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{15}{16} } & & \\ & V = \left\{ \frac{15}{16} \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{-1}& = & 14 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{-1}\color{blue}{+1+5x } & = & 14 \color{red}{ -5x }\color{blue}{+1+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & 14 \color{blue}{+1} \\\Leftrightarrow &11x & = &15\\\Leftrightarrow & \color{red}{11}x & = &15\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{15}{11} \\\Leftrightarrow & \color{green}{ x = \frac{15}{11} } & & \\ & V = \left\{ \frac{15}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{-8}& = & 14 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{-8}\color{blue}{+8-11x } & = & 14 \color{red}{ +11x }\color{blue}{+8-11x } \\\Leftrightarrow & -5x \color{blue}{-11x } & = & 14 \color{blue}{+8} \\\Leftrightarrow &-16x & = &22\\\Leftrightarrow & \color{red}{-16}x & = &22\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{22}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{8} } & & \\ & V = \left\{ \frac{-11}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & 3x \color{red}{-4}& = & -3 \color{red}{ +4x } \\\Leftrightarrow & 3x \color{red}{-4}\color{blue}{+4-4x } & = & -3 \color{red}{ +4x }\color{blue}{+4-4x } \\\Leftrightarrow & 3x \color{blue}{-4x } & = & -3 \color{blue}{+4} \\\Leftrightarrow &-x & = &1\\\Leftrightarrow & \color{red}{-}x & = &1\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{1}{-1} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
12. \(\begin{align} & x \color{red}{+10}& = & 12 \color{red}{ +6x } \\\Leftrightarrow & x \color{red}{+10}\color{blue}{-10-6x } & = & 12 \color{red}{ +6x }\color{blue}{-10-6x } \\\Leftrightarrow & x \color{blue}{-6x } & = & 12 \color{blue}{-10} \\\Leftrightarrow &-5x & = &2\\\Leftrightarrow & \color{red}{-5}x & = &2\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{2}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)