Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 7x \color{red}{-10}& = & -2 \color{red}{ +11x } \\\Leftrightarrow & 7x \color{red}{-10}\color{blue}{+10-11x } & = & -2 \color{red}{ +11x }\color{blue}{+10-11x } \\\Leftrightarrow & 7x \color{blue}{-11x } & = & -2 \color{blue}{+10} \\\Leftrightarrow &-4x & = &8\\\Leftrightarrow & \color{red}{-4}x & = &8\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{8}{-4} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
2. \(\begin{align} & -14x \color{red}{-5}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-5}\color{blue}{+5-x } & = & 14 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 14 \color{blue}{+5} \\\Leftrightarrow &-15x & = &19\\\Leftrightarrow & \color{red}{-15}x & = &19\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{19}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{15} } & & \\ & V = \left\{ \frac{-19}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & -14x \color{red}{+2}& = & -15 \color{red}{ +3x } \\\Leftrightarrow & -14x \color{red}{+2}\color{blue}{-2-3x } & = & -15 \color{red}{ +3x }\color{blue}{-2-3x } \\\Leftrightarrow & -14x \color{blue}{-3x } & = & -15 \color{blue}{-2} \\\Leftrightarrow &-17x & = &-17\\\Leftrightarrow & \color{red}{-17}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-17}{-17} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
4. \(\begin{align} & -13x \color{red}{-11}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-11}\color{blue}{+11-x } & = & 7 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 7 \color{blue}{+11} \\\Leftrightarrow &-14x & = &18\\\Leftrightarrow & \color{red}{-14}x & = &18\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{18}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -15x \color{red}{+1}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+1}\color{blue}{-1-x } & = & -9 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -9 \color{blue}{-1} \\\Leftrightarrow &-16x & = &-10\\\Leftrightarrow & \color{red}{-16}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-10}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{5}{8} } & & \\ & V = \left\{ \frac{5}{8} \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{+4}& = & -2 \color{red}{ +6x } \\\Leftrightarrow & -11x \color{red}{+4}\color{blue}{-4-6x } & = & -2 \color{red}{ +6x }\color{blue}{-4-6x } \\\Leftrightarrow & -11x \color{blue}{-6x } & = & -2 \color{blue}{-4} \\\Leftrightarrow &-17x & = &-6\\\Leftrightarrow & \color{red}{-17}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-6}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{6}{17} } & & \\ & V = \left\{ \frac{6}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & 15x \color{red}{+7}& = & -7 \color{red}{ +4x } \\\Leftrightarrow & 15x \color{red}{+7}\color{blue}{-7-4x } & = & -7 \color{red}{ +4x }\color{blue}{-7-4x } \\\Leftrightarrow & 15x \color{blue}{-4x } & = & -7 \color{blue}{-7} \\\Leftrightarrow &11x & = &-14\\\Leftrightarrow & \color{red}{11}x & = &-14\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-14}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{11} } & & \\ & V = \left\{ \frac{-14}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -2x \color{red}{-6}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-6}\color{blue}{+6-x } & = & -13 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -13 \color{blue}{+6} \\\Leftrightarrow &-3x & = &-7\\\Leftrightarrow & \color{red}{-3}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-7}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{+4}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+4}\color{blue}{-4-x } & = & -13 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -13 \color{blue}{-4} \\\Leftrightarrow &-11x & = &-17\\\Leftrightarrow & \color{red}{-11}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-17}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{17}{11} } & & \\ & V = \left\{ \frac{17}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{+9}& = & 3 \color{red}{ +3x } \\\Leftrightarrow & 14x \color{red}{+9}\color{blue}{-9-3x } & = & 3 \color{red}{ +3x }\color{blue}{-9-3x } \\\Leftrightarrow & 14x \color{blue}{-3x } & = & 3 \color{blue}{-9} \\\Leftrightarrow &11x & = &-6\\\Leftrightarrow & \color{red}{11}x & = &-6\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-6}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{11} } & & \\ & V = \left\{ \frac{-6}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -13x \color{red}{+2}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+2}\color{blue}{-2-x } & = & -14 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -14 \color{blue}{-2} \\\Leftrightarrow &-14x & = &-16\\\Leftrightarrow & \color{red}{-14}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-16}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{8}{7} } & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{-10}& = & -13 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{-10}\color{blue}{+10+13x } & = & -13 \color{red}{ -13x }\color{blue}{+10+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & -13 \color{blue}{+10} \\\Leftrightarrow &24x & = &-3\\\Leftrightarrow & \color{red}{24}x & = &-3\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{-3}{24} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)