Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -11x \color{red}{-9}& = & 8 \color{red}{ +3x } \\\Leftrightarrow & -11x \color{red}{-9}\color{blue}{+9-3x } & = & 8 \color{red}{ +3x }\color{blue}{+9-3x } \\\Leftrightarrow & -11x \color{blue}{-3x } & = & 8 \color{blue}{+9} \\\Leftrightarrow &-14x & = &17\\\Leftrightarrow & \color{red}{-14}x & = &17\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{17}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{14} } & & \\ & V = \left\{ \frac{-17}{14} \right\} & \\\end{align}\)
2. \(\begin{align} & -4x \color{red}{-11}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-11}\color{blue}{+11-x } & = & 4 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 4 \color{blue}{+11} \\\Leftrightarrow &-5x & = &15\\\Leftrightarrow & \color{red}{-5}x & = &15\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{15}{-5} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{+10}& = & 6 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{+10}\color{blue}{-10+7x } & = & 6 \color{red}{ -7x }\color{blue}{-10+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & 6 \color{blue}{-10} \\\Leftrightarrow &22x & = &-4\\\Leftrightarrow & \color{red}{22}x & = &-4\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-4}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{11} } & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & -5x \color{red}{+5}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+5}\color{blue}{-5-x } & = & -5 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -5 \color{blue}{-5} \\\Leftrightarrow &-6x & = &-10\\\Leftrightarrow & \color{red}{-6}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-10}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & -7x \color{red}{+9}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+9}\color{blue}{-9-x } & = & -13 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -13 \color{blue}{-9} \\\Leftrightarrow &-8x & = &-22\\\Leftrightarrow & \color{red}{-8}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-22}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{11}{4} } & & \\ & V = \left\{ \frac{11}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{-3}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-3}\color{blue}{+3-x } & = & 12 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 12 \color{blue}{+3} \\\Leftrightarrow &-14x & = &15\\\Leftrightarrow & \color{red}{-14}x & = &15\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{15}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{14} } & & \\ & V = \left\{ \frac{-15}{14} \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{-2}& = & -2 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{-2}\color{blue}{+2-6x } & = & -2 \color{red}{ +6x }\color{blue}{+2-6x } \\\Leftrightarrow & -5x \color{blue}{-6x } & = & -2 \color{blue}{+2} \\\Leftrightarrow &-11x & = &0\\\Leftrightarrow & \color{red}{-11}x & = &0\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{0}{-11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{-12}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-12}\color{blue}{+12-x } & = & -7 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -7 \color{blue}{+12} \\\Leftrightarrow &-8x & = &5\\\Leftrightarrow & \color{red}{-8}x & = &5\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{5}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{8} } & & \\ & V = \left\{ \frac{-5}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{-12}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-12}\color{blue}{+12-x } & = & 9 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 9 \color{blue}{+12} \\\Leftrightarrow &-7x & = &21\\\Leftrightarrow & \color{red}{-7}x & = &21\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{21}{-7} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
10. \(\begin{align} & -7x \color{red}{+5}& = & -2 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{+5}\color{blue}{-5-11x } & = & -2 \color{red}{ +11x }\color{blue}{-5-11x } \\\Leftrightarrow & -7x \color{blue}{-11x } & = & -2 \color{blue}{-5} \\\Leftrightarrow &-18x & = &-7\\\Leftrightarrow & \color{red}{-18}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{-7}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{7}{18} } & & \\ & V = \left\{ \frac{7}{18} \right\} & \\\end{align}\)
11. \(\begin{align} & -13x \color{red}{-9}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-9}\color{blue}{+9-x } & = & 15 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 15 \color{blue}{+9} \\\Leftrightarrow &-14x & = &24\\\Leftrightarrow & \color{red}{-14}x & = &24\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{24}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{7} } & & \\ & V = \left\{ \frac{-12}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -5x \color{red}{+10}& = & 10 \color{red}{ +8x } \\\Leftrightarrow & -5x \color{red}{+10}\color{blue}{-10-8x } & = & 10 \color{red}{ +8x }\color{blue}{-10-8x } \\\Leftrightarrow & -5x \color{blue}{-8x } & = & 10 \color{blue}{-10} \\\Leftrightarrow &-13x & = &0\\\Leftrightarrow & \color{red}{-13}x & = &0\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{0}{-13} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)