Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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