Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 6x \color{red}{-3}& = & -9 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{-3}\color{blue}{+3-11x } & = & -9 \color{red}{ +11x }\color{blue}{+3-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & -9 \color{blue}{+3} \\\Leftrightarrow &-5x & = &-6\\\Leftrightarrow & \color{red}{-5}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-6}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{6}{5} } & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{-11}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-11}\color{blue}{+11-x } & = & 15 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 15 \color{blue}{+11} \\\Leftrightarrow &-11x & = &26\\\Leftrightarrow & \color{red}{-11}x & = &26\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{26}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{11} } & & \\ & V = \left\{ \frac{-26}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & -x \color{red}{+1}& = & 6 \color{red}{ -6x } \\\Leftrightarrow & -x \color{red}{+1}\color{blue}{-1+6x } & = & 6 \color{red}{ -6x }\color{blue}{-1+6x } \\\Leftrightarrow & -x \color{blue}{+6x } & = & 6 \color{blue}{-1} \\\Leftrightarrow &5x & = &5\\\Leftrightarrow & \color{red}{5}x & = &5\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{5}{5} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{+11}& = & 6 \color{red}{ -2x } \\\Leftrightarrow & 13x \color{red}{+11}\color{blue}{-11+2x } & = & 6 \color{red}{ -2x }\color{blue}{-11+2x } \\\Leftrightarrow & 13x \color{blue}{+2x } & = & 6 \color{blue}{-11} \\\Leftrightarrow &15x & = &-5\\\Leftrightarrow & \color{red}{15}x & = &-5\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-5}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & -11x \color{red}{+1}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+1}\color{blue}{-1-x } & = & -6 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -6 \color{blue}{-1} \\\Leftrightarrow &-12x & = &-7\\\Leftrightarrow & \color{red}{-12}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-7}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{12} } & & \\ & V = \left\{ \frac{7}{12} \right\} & \\\end{align}\)
6. \(\begin{align} & -7x \color{red}{-5}& = & -3 \color{red}{ +4x } \\\Leftrightarrow & -7x \color{red}{-5}\color{blue}{+5-4x } & = & -3 \color{red}{ +4x }\color{blue}{+5-4x } \\\Leftrightarrow & -7x \color{blue}{-4x } & = & -3 \color{blue}{+5} \\\Leftrightarrow &-11x & = &2\\\Leftrightarrow & \color{red}{-11}x & = &2\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{2}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{11} } & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & 4x \color{red}{-7}& = & 5 \color{red}{ +9x } \\\Leftrightarrow & 4x \color{red}{-7}\color{blue}{+7-9x } & = & 5 \color{red}{ +9x }\color{blue}{+7-9x } \\\Leftrightarrow & 4x \color{blue}{-9x } & = & 5 \color{blue}{+7} \\\Leftrightarrow &-5x & = &12\\\Leftrightarrow & \color{red}{-5}x & = &12\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{12}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{5} } & & \\ & V = \left\{ \frac{-12}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 12x \color{red}{+15}& = & -11 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{+15}\color{blue}{-15-5x } & = & -11 \color{red}{ +5x }\color{blue}{-15-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & -11 \color{blue}{-15} \\\Leftrightarrow &7x & = &-26\\\Leftrightarrow & \color{red}{7}x & = &-26\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-26}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{7} } & & \\ & V = \left\{ \frac{-26}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -x \color{red}{+3}& = & -15 \color{red}{ -10x } \\\Leftrightarrow & -x \color{red}{+3}\color{blue}{-3+10x } & = & -15 \color{red}{ -10x }\color{blue}{-3+10x } \\\Leftrightarrow & -x \color{blue}{+10x } & = & -15 \color{blue}{-3} \\\Leftrightarrow &9x & = &-18\\\Leftrightarrow & \color{red}{9}x & = &-18\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-18}{9} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
10. \(\begin{align} & 15x \color{red}{-7}& = & 13 \color{red}{ +11x } \\\Leftrightarrow & 15x \color{red}{-7}\color{blue}{+7-11x } & = & 13 \color{red}{ +11x }\color{blue}{+7-11x } \\\Leftrightarrow & 15x \color{blue}{-11x } & = & 13 \color{blue}{+7} \\\Leftrightarrow &4x & = &20\\\Leftrightarrow & \color{red}{4}x & = &20\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{20}{4} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
11. \(\begin{align} & -11x \color{red}{-4}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-4}\color{blue}{+4-x } & = & 12 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 12 \color{blue}{+4} \\\Leftrightarrow &-12x & = &16\\\Leftrightarrow & \color{red}{-12}x & = &16\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{16}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -15x \color{red}{+8}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+8}\color{blue}{-8-x } & = & -3 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -3 \color{blue}{-8} \\\Leftrightarrow &-16x & = &-11\\\Leftrightarrow & \color{red}{-16}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-11}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{11}{16} } & & \\ & V = \left\{ \frac{11}{16} \right\} & \\\end{align}\)