Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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