Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 9x \color{red}{-9}& = & -8 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{-9}\color{blue}{+9+13x } & = & -8 \color{red}{ -13x }\color{blue}{+9+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & -8 \color{blue}{+9} \\\Leftrightarrow &22x & = &1\\\Leftrightarrow & \color{red}{22}x & = &1\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{1}{22} \\\Leftrightarrow & \color{green}{ x = \frac{1}{22} } & & \\ & V = \left\{ \frac{1}{22} \right\} & \\\end{align}\)
2. \(\begin{align} & -4x \color{red}{+11}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+11}\color{blue}{-11-x } & = & 8 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 8 \color{blue}{-11} \\\Leftrightarrow &-5x & = &-3\\\Leftrightarrow & \color{red}{-5}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-3}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 14x \color{red}{+6}& = & -10 \color{red}{ +3x } \\\Leftrightarrow & 14x \color{red}{+6}\color{blue}{-6-3x } & = & -10 \color{red}{ +3x }\color{blue}{-6-3x } \\\Leftrightarrow & 14x \color{blue}{-3x } & = & -10 \color{blue}{-6} \\\Leftrightarrow &11x & = &-16\\\Leftrightarrow & \color{red}{11}x & = &-16\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-16}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{11} } & & \\ & V = \left\{ \frac{-16}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & -14x \color{red}{-12}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-12}\color{blue}{+12-x } & = & -10 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -10 \color{blue}{+12} \\\Leftrightarrow &-15x & = &2\\\Leftrightarrow & \color{red}{-15}x & = &2\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{2}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{15} } & & \\ & V = \left\{ \frac{-2}{15} \right\} & \\\end{align}\)
5. \(\begin{align} & -13x \color{red}{-1}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-1}\color{blue}{+1-x } & = & 9 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 9 \color{blue}{+1} \\\Leftrightarrow &-14x & = &10\\\Leftrightarrow & \color{red}{-14}x & = &10\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{10}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -5x \color{red}{-11}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-11}\color{blue}{+11-x } & = & -13 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -13 \color{blue}{+11} \\\Leftrightarrow &-6x & = &-2\\\Leftrightarrow & \color{red}{-6}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-2}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -7x \color{red}{+6}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+6}\color{blue}{-6-x } & = & -12 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -12 \color{blue}{-6} \\\Leftrightarrow &-8x & = &-18\\\Leftrightarrow & \color{red}{-8}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-18}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{9}{4} } & & \\ & V = \left\{ \frac{9}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & 2x \color{red}{-10}& = & -11 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-10}\color{blue}{+10-x } & = & -11 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -11 \color{blue}{+10} \\\Leftrightarrow &x & = &-1\\\Leftrightarrow & \color{red}{}x & = &-1\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -1 \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{+13}& = & 6 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+13}\color{blue}{-13-13x } & = & 6 \color{red}{ +13x }\color{blue}{-13-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 6 \color{blue}{-13} \\\Leftrightarrow &-19x & = &-7\\\Leftrightarrow & \color{red}{-19}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-7}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{7}{19} } & & \\ & V = \left\{ \frac{7}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & -15x \color{red}{+8}& = & 12 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{+8}\color{blue}{-8-8x } & = & 12 \color{red}{ +8x }\color{blue}{-8-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & 12 \color{blue}{-8} \\\Leftrightarrow &-23x & = &4\\\Leftrightarrow & \color{red}{-23}x & = &4\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{4}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{23} } & & \\ & V = \left\{ \frac{-4}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{-5}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-5}\color{blue}{+5-x } & = & -7 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -7 \color{blue}{+5} \\\Leftrightarrow &-11x & = &-2\\\Leftrightarrow & \color{red}{-11}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-2}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{2}{11} } & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{+15}& = & -8 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{+15}\color{blue}{-15-5x } & = & -8 \color{red}{ +5x }\color{blue}{-15-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & -8 \color{blue}{-15} \\\Leftrightarrow &-14x & = &-23\\\Leftrightarrow & \color{red}{-14}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-23}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{23}{14} } & & \\ & V = \left\{ \frac{23}{14} \right\} & \\\end{align}\)