Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -5x \color{red}{-11}& = & 6 \color{red}{ +3x } \\\Leftrightarrow & -5x \color{red}{-11}\color{blue}{+11-3x } & = & 6 \color{red}{ +3x }\color{blue}{+11-3x } \\\Leftrightarrow & -5x \color{blue}{-3x } & = & 6 \color{blue}{+11} \\\Leftrightarrow &-8x & = &17\\\Leftrightarrow & \color{red}{-8}x & = &17\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{17}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{8} } & & \\ & V = \left\{ \frac{-17}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{-9}& = & 8 \color{red}{ +7x } \\\Leftrightarrow & 15x \color{red}{-9}\color{blue}{+9-7x } & = & 8 \color{red}{ +7x }\color{blue}{+9-7x } \\\Leftrightarrow & 15x \color{blue}{-7x } & = & 8 \color{blue}{+9} \\\Leftrightarrow &8x & = &17\\\Leftrightarrow & \color{red}{8}x & = &17\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{17}{8} \\\Leftrightarrow & \color{green}{ x = \frac{17}{8} } & & \\ & V = \left\{ \frac{17}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & 6x \color{red}{+8}& = & -13 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+8}\color{blue}{-8+5x } & = & -13 \color{red}{ -5x }\color{blue}{-8+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & -13 \color{blue}{-8} \\\Leftrightarrow &11x & = &-21\\\Leftrightarrow & \color{red}{11}x & = &-21\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-21}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{11} } & & \\ & V = \left\{ \frac{-21}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & -3x \color{red}{+5}& = & -2 \color{red}{ +13x } \\\Leftrightarrow & -3x \color{red}{+5}\color{blue}{-5-13x } & = & -2 \color{red}{ +13x }\color{blue}{-5-13x } \\\Leftrightarrow & -3x \color{blue}{-13x } & = & -2 \color{blue}{-5} \\\Leftrightarrow &-16x & = &-7\\\Leftrightarrow & \color{red}{-16}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-7}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{7}{16} } & & \\ & V = \left\{ \frac{7}{16} \right\} & \\\end{align}\)
5. \(\begin{align} & -12x \color{red}{-15}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-15}\color{blue}{+15-x } & = & 7 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 7 \color{blue}{+15} \\\Leftrightarrow &-13x & = &22\\\Leftrightarrow & \color{red}{-13}x & = &22\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{22}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{13} } & & \\ & V = \left\{ \frac{-22}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{-10}& = & 4 \color{red}{ +11x } \\\Leftrightarrow & 8x \color{red}{-10}\color{blue}{+10-11x } & = & 4 \color{red}{ +11x }\color{blue}{+10-11x } \\\Leftrightarrow & 8x \color{blue}{-11x } & = & 4 \color{blue}{+10} \\\Leftrightarrow &-3x & = &14\\\Leftrightarrow & \color{red}{-3}x & = &14\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{14}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{3} } & & \\ & V = \left\{ \frac{-14}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -8x \color{red}{+2}& = & -6 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+2}\color{blue}{-2-9x } & = & -6 \color{red}{ +9x }\color{blue}{-2-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & -6 \color{blue}{-2} \\\Leftrightarrow &-17x & = &-8\\\Leftrightarrow & \color{red}{-17}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-8}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{8}{17} } & & \\ & V = \left\{ \frac{8}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & 8x \color{red}{-8}& = & -15 \color{red}{ -13x } \\\Leftrightarrow & 8x \color{red}{-8}\color{blue}{+8+13x } & = & -15 \color{red}{ -13x }\color{blue}{+8+13x } \\\Leftrightarrow & 8x \color{blue}{+13x } & = & -15 \color{blue}{+8} \\\Leftrightarrow &21x & = &-7\\\Leftrightarrow & \color{red}{21}x & = &-7\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{-7}{21} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{-6}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-6}\color{blue}{+6-x } & = & -12 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -12 \color{blue}{+6} \\\Leftrightarrow &-14x & = &-6\\\Leftrightarrow & \color{red}{-14}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-6}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{3}{7} } & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{-8}& = & 6 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-8}\color{blue}{+8+13x } & = & 6 \color{red}{ -13x }\color{blue}{+8+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & 6 \color{blue}{+8} \\\Leftrightarrow &27x & = &14\\\Leftrightarrow & \color{red}{27}x & = &14\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{14}{27} \\\Leftrightarrow & \color{green}{ x = \frac{14}{27} } & & \\ & V = \left\{ \frac{14}{27} \right\} & \\\end{align}\)
11. \(\begin{align} & -x \color{red}{-13}& = & 1 \color{red}{ +2x } \\\Leftrightarrow & -x \color{red}{-13}\color{blue}{+13-2x } & = & 1 \color{red}{ +2x }\color{blue}{+13-2x } \\\Leftrightarrow & -x \color{blue}{-2x } & = & 1 \color{blue}{+13} \\\Leftrightarrow &-3x & = &14\\\Leftrightarrow & \color{red}{-3}x & = &14\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{14}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{3} } & & \\ & V = \left\{ \frac{-14}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{+15}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+15}\color{blue}{-15-x } & = & -7 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -7 \color{blue}{-15} \\\Leftrightarrow &-15x & = &-22\\\Leftrightarrow & \color{red}{-15}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-22}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{22}{15} } & & \\ & V = \left\{ \frac{22}{15} \right\} & \\\end{align}\)