Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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