Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -x \color{red}{+11}& = & -12 \color{red}{ -7x } \\\Leftrightarrow & -x \color{red}{+11}\color{blue}{-11+7x } & = & -12 \color{red}{ -7x }\color{blue}{-11+7x } \\\Leftrightarrow & -x \color{blue}{+7x } & = & -12 \color{blue}{-11} \\\Leftrightarrow &6x & = &-23\\\Leftrightarrow & \color{red}{6}x & = &-23\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{-23}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{6} } & & \\ & V = \left\{ \frac{-23}{6} \right\} & \\\end{align}\)
2. \(\begin{align} & 10x \color{red}{+15}& = & -14 \color{red}{ +11x } \\\Leftrightarrow & 10x \color{red}{+15}\color{blue}{-15-11x } & = & -14 \color{red}{ +11x }\color{blue}{-15-11x } \\\Leftrightarrow & 10x \color{blue}{-11x } & = & -14 \color{blue}{-15} \\\Leftrightarrow &-x & = &-29\\\Leftrightarrow & \color{red}{-}x & = &-29\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-29}{-1} \\\Leftrightarrow & \color{green}{ x = 29 } & & \\ & V = \left\{ 29 \right\} & \\\end{align}\)
3. \(\begin{align} & -8x \color{red}{+2}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+2}\color{blue}{-2-x } & = & -15 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -15 \color{blue}{-2} \\\Leftrightarrow &-9x & = &-17\\\Leftrightarrow & \color{red}{-9}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-17}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{17}{9} } & & \\ & V = \left\{ \frac{17}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & -14x \color{red}{-13}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-13}\color{blue}{+13-x } & = & -1 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -1 \color{blue}{+13} \\\Leftrightarrow &-15x & = &12\\\Leftrightarrow & \color{red}{-15}x & = &12\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{12}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -7x \color{red}{+2}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+2}\color{blue}{-2-x } & = & -13 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -13 \color{blue}{-2} \\\Leftrightarrow &-8x & = &-15\\\Leftrightarrow & \color{red}{-8}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-15}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{15}{8} } & & \\ & V = \left\{ \frac{15}{8} \right\} & \\\end{align}\)
6. \(\begin{align} & -x \color{red}{+11}& = & -1 \color{red}{ +14x } \\\Leftrightarrow & -x \color{red}{+11}\color{blue}{-11-14x } & = & -1 \color{red}{ +14x }\color{blue}{-11-14x } \\\Leftrightarrow & -x \color{blue}{-14x } & = & -1 \color{blue}{-11} \\\Leftrightarrow &-15x & = &-12\\\Leftrightarrow & \color{red}{-15}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-12}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{+15}& = & 12 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+15}\color{blue}{-15-x } & = & 12 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 12 \color{blue}{-15} \\\Leftrightarrow &11x & = &-3\\\Leftrightarrow & \color{red}{11}x & = &-3\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-3}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{11} } & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 13x \color{red}{-6}& = & -8 \color{red}{ -15x } \\\Leftrightarrow & 13x \color{red}{-6}\color{blue}{+6+15x } & = & -8 \color{red}{ -15x }\color{blue}{+6+15x } \\\Leftrightarrow & 13x \color{blue}{+15x } & = & -8 \color{blue}{+6} \\\Leftrightarrow &28x & = &-2\\\Leftrightarrow & \color{red}{28}x & = &-2\\\Leftrightarrow & \frac{\color{red}{28}x}{ \color{blue}{ 28}} & = & \frac{-2}{28} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{14} } & & \\ & V = \left\{ \frac{-1}{14} \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{+9}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+9}\color{blue}{-9-x } & = & 6 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 6 \color{blue}{-9} \\\Leftrightarrow &-12x & = &-3\\\Leftrightarrow & \color{red}{-12}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-3}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & 4x \color{red}{-12}& = & -12 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{-12}\color{blue}{+12+11x } & = & -12 \color{red}{ -11x }\color{blue}{+12+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & -12 \color{blue}{+12} \\\Leftrightarrow &15x & = &0\\\Leftrightarrow & \color{red}{15}x & = &0\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{0}{15} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & -7x \color{red}{-14}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-14}\color{blue}{+14-x } & = & -10 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -10 \color{blue}{+14} \\\Leftrightarrow &-8x & = &4\\\Leftrightarrow & \color{red}{-8}x & = &4\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{4}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & 15x \color{red}{-8}& = & -2 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{-8}\color{blue}{+8+7x } & = & -2 \color{red}{ -7x }\color{blue}{+8+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & -2 \color{blue}{+8} \\\Leftrightarrow &22x & = &6\\\Leftrightarrow & \color{red}{22}x & = &6\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{6}{22} \\\Leftrightarrow & \color{green}{ x = \frac{3}{11} } & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)