Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -10x \color{red}{-10}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-10}\color{blue}{+10-x } & = & -15 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -15 \color{blue}{+10} \\\Leftrightarrow &-11x & = &-5\\\Leftrightarrow & \color{red}{-11}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-5}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{5}{11} } & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{-6}& = & -11 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{-6}\color{blue}{+6-8x } & = & -11 \color{red}{ +8x }\color{blue}{+6-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & -11 \color{blue}{+6} \\\Leftrightarrow &-23x & = &-5\\\Leftrightarrow & \color{red}{-23}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-5}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{5}{23} } & & \\ & V = \left\{ \frac{5}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & -6x \color{red}{-2}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-2}\color{blue}{+2-x } & = & -15 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -15 \color{blue}{+2} \\\Leftrightarrow &-7x & = &-13\\\Leftrightarrow & \color{red}{-7}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-13}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{13}{7} } & & \\ & V = \left\{ \frac{13}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & -13x \color{red}{-1}& = & -7 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{-1}\color{blue}{+1-14x } & = & -7 \color{red}{ +14x }\color{blue}{+1-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & -7 \color{blue}{+1} \\\Leftrightarrow &-27x & = &-6\\\Leftrightarrow & \color{red}{-27}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{-6}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{2}{9} } & & \\ & V = \left\{ \frac{2}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{+8}& = & -7 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{+8}\color{blue}{-8-x } & = & -7 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & -7 \color{blue}{-8} \\\Leftrightarrow &9x & = &-15\\\Leftrightarrow & \color{red}{9}x & = &-15\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-15}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{-2}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-2}\color{blue}{+2-x } & = & -14 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -14 \color{blue}{+2} \\\Leftrightarrow &-11x & = &-12\\\Leftrightarrow & \color{red}{-11}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-12}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{12}{11} } & & \\ & V = \left\{ \frac{12}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & -13x \color{red}{+6}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+6}\color{blue}{-6-x } & = & -10 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -10 \color{blue}{-6} \\\Leftrightarrow &-14x & = &-16\\\Leftrightarrow & \color{red}{-14}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-16}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{8}{7} } & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{-11}& = & 7 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{-11}\color{blue}{+11+11x } & = & 7 \color{red}{ -11x }\color{blue}{+11+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & 7 \color{blue}{+11} \\\Leftrightarrow &15x & = &18\\\Leftrightarrow & \color{red}{15}x & = &18\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{18}{15} \\\Leftrightarrow & \color{green}{ x = \frac{6}{5} } & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{-2}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-2}\color{blue}{+2-x } & = & -14 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -14 \color{blue}{+2} \\\Leftrightarrow &-12x & = &-12\\\Leftrightarrow & \color{red}{-12}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-12}{-12} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
10. \(\begin{align} & 8x \color{red}{+11}& = & -8 \color{red}{ +11x } \\\Leftrightarrow & 8x \color{red}{+11}\color{blue}{-11-11x } & = & -8 \color{red}{ +11x }\color{blue}{-11-11x } \\\Leftrightarrow & 8x \color{blue}{-11x } & = & -8 \color{blue}{-11} \\\Leftrightarrow &-3x & = &-19\\\Leftrightarrow & \color{red}{-3}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-19}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{19}{3} } & & \\ & V = \left\{ \frac{19}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -x \color{red}{-9}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -x \color{red}{-9}\color{blue}{+9-x } & = & -5 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -x \color{blue}{-x } & = & -5 \color{blue}{+9} \\\Leftrightarrow &-2x & = &4\\\Leftrightarrow & \color{red}{-2}x & = &4\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{4}{-2} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{-14}& = & 3 \color{red}{ +12x } \\\Leftrightarrow & -x \color{red}{-14}\color{blue}{+14-12x } & = & 3 \color{red}{ +12x }\color{blue}{+14-12x } \\\Leftrightarrow & -x \color{blue}{-12x } & = & 3 \color{blue}{+14} \\\Leftrightarrow &-13x & = &17\\\Leftrightarrow & \color{red}{-13}x & = &17\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{17}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{13} } & & \\ & V = \left\{ \frac{-17}{13} \right\} & \\\end{align}\)