Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -2x \color{red}{-7}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-7}\color{blue}{+7-x } & = & 4 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 4 \color{blue}{+7} \\\Leftrightarrow &-3x & = &11\\\Leftrightarrow & \color{red}{-3}x & = &11\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{11}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{3} } & & \\ & V = \left\{ \frac{-11}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -5x \color{red}{+6}& = & -14 \color{red}{ +3x } \\\Leftrightarrow & -5x \color{red}{+6}\color{blue}{-6-3x } & = & -14 \color{red}{ +3x }\color{blue}{-6-3x } \\\Leftrightarrow & -5x \color{blue}{-3x } & = & -14 \color{blue}{-6} \\\Leftrightarrow &-8x & = &-20\\\Leftrightarrow & \color{red}{-8}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-20}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & 5x \color{red}{+6}& = & -2 \color{red}{ -4x } \\\Leftrightarrow & 5x \color{red}{+6}\color{blue}{-6+4x } & = & -2 \color{red}{ -4x }\color{blue}{-6+4x } \\\Leftrightarrow & 5x \color{blue}{+4x } & = & -2 \color{blue}{-6} \\\Leftrightarrow &9x & = &-8\\\Leftrightarrow & \color{red}{9}x & = &-8\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-8}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{9} } & & \\ & V = \left\{ \frac{-8}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & -8x \color{red}{-11}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-11}\color{blue}{+11-x } & = & 12 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 12 \color{blue}{+11} \\\Leftrightarrow &-9x & = &23\\\Leftrightarrow & \color{red}{-9}x & = &23\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{23}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{9} } & & \\ & V = \left\{ \frac{-23}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & -15x \color{red}{+7}& = & 6 \color{red}{ +4x } \\\Leftrightarrow & -15x \color{red}{+7}\color{blue}{-7-4x } & = & 6 \color{red}{ +4x }\color{blue}{-7-4x } \\\Leftrightarrow & -15x \color{blue}{-4x } & = & 6 \color{blue}{-7} \\\Leftrightarrow &-19x & = &-1\\\Leftrightarrow & \color{red}{-19}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-1}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{1}{19} } & & \\ & V = \left\{ \frac{1}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{+9}& = & 12 \color{red}{ +7x } \\\Leftrightarrow & 8x \color{red}{+9}\color{blue}{-9-7x } & = & 12 \color{red}{ +7x }\color{blue}{-9-7x } \\\Leftrightarrow & 8x \color{blue}{-7x } & = & 12 \color{blue}{-9} \\\Leftrightarrow &x & = &3\\\Leftrightarrow & \color{red}{}x & = &3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 3 \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{+1}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+1}\color{blue}{-1-x } & = & 3 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 3 \color{blue}{-1} \\\Leftrightarrow &-11x & = &2\\\Leftrightarrow & \color{red}{-11}x & = &2\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{2}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{11} } & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 2x \color{red}{+15}& = & -7 \color{red}{ +11x } \\\Leftrightarrow & 2x \color{red}{+15}\color{blue}{-15-11x } & = & -7 \color{red}{ +11x }\color{blue}{-15-11x } \\\Leftrightarrow & 2x \color{blue}{-11x } & = & -7 \color{blue}{-15} \\\Leftrightarrow &-9x & = &-22\\\Leftrightarrow & \color{red}{-9}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-22}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{22}{9} } & & \\ & V = \left\{ \frac{22}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & -8x \color{red}{-13}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-13}\color{blue}{+13-x } & = & -7 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -7 \color{blue}{+13} \\\Leftrightarrow &-9x & = &6\\\Leftrightarrow & \color{red}{-9}x & = &6\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{6}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -10x \color{red}{+1}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+1}\color{blue}{-1-x } & = & -7 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -7 \color{blue}{-1} \\\Leftrightarrow &-11x & = &-8\\\Leftrightarrow & \color{red}{-11}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-8}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{8}{11} } & & \\ & V = \left\{ \frac{8}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -11x \color{red}{-14}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-14}\color{blue}{+14-x } & = & -1 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -1 \color{blue}{+14} \\\Leftrightarrow &-12x & = &13\\\Leftrightarrow & \color{red}{-12}x & = &13\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{13}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{12} } & & \\ & V = \left\{ \frac{-13}{12} \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{+3}& = & 14 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{+3}\color{blue}{-3+13x } & = & 14 \color{red}{ -13x }\color{blue}{-3+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & 14 \color{blue}{-3} \\\Leftrightarrow &22x & = &11\\\Leftrightarrow & \color{red}{22}x & = &11\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{11}{22} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)