Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (4x+3)& = & 9 \color{red}{-} (10+3x) \\\Leftrightarrow & 20x+15& = &9-10-3x \\\Leftrightarrow & 20x \color{red}{+15} & = &-1 \color{red}{-3x} \\\Leftrightarrow & 20x \color{red}{+15} \color{blue}{-15} \color{blue}{+3x} & = &-1 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-15} \\\Leftrightarrow & 20x+3x& = &-1-15 \\\Leftrightarrow & 23x& = &-16 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-16}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-16}{23} & & \\ & V = \left\{ \frac{-16}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (4x+3)& = & -4 \color{red}{+} (-7+x) \\\Leftrightarrow & 12x+9& = &-4-7+x \\\Leftrightarrow & 12x \color{red}{+9} & = &-11 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+9} \color{blue}{-9} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{-9} \\\Leftrightarrow & 12x-x& = &-11-9 \\\Leftrightarrow & 11x& = &-20 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-20}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-20}{11} & & \\ & V = \left\{ \frac{-20}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (2x-2)& = & -11 \color{red}{-} (-12+3x) \\\Leftrightarrow & 10x-10& = &-11+12-3x \\\Leftrightarrow & 10x \color{red}{-10} & = &1 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{-10} \color{blue}{+10} \color{blue}{+3x} & = &1 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+10} \\\Leftrightarrow & 10x+3x& = &1+10 \\\Leftrightarrow & 13x& = &11 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{11}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{11}{13} & & \\ & V = \left\{ \frac{11}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (5x-6)& = & 2 \color{red}{+} (9+x) \\\Leftrightarrow & 30x-36& = &2+9+x \\\Leftrightarrow & 30x \color{red}{-36} & = &11 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-36} \color{blue}{+36} \color{blue}{-x} & = &11 \color{red}{+x} \color{blue}{-x} \color{blue}{+36} \\\Leftrightarrow & 30x-x& = &11+36 \\\Leftrightarrow & 29x& = &47 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{47}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{47}{29} & & \\ & V = \left\{ \frac{47}{29} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (3x+2)& = & 11 \color{red}{+} (-14-2x) \\\Leftrightarrow & 15x+10& = &11-14-2x \\\Leftrightarrow & 15x \color{red}{+10} & = &-3 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{+10} \color{blue}{-10} \color{blue}{+2x} & = &-3 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-10} \\\Leftrightarrow & 15x+2x& = &-3-10 \\\Leftrightarrow & 17x& = &-13 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-13}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-13}{17} & & \\ & V = \left\{ \frac{-13}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (x+7)& = & -14 \color{red}{-} (13-5x) \\\Leftrightarrow & 6x+42& = &-14-13+5x \\\Leftrightarrow & 6x \color{red}{+42} & = &-27 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+42} \color{blue}{-42} \color{blue}{-5x} & = &-27 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-42} \\\Leftrightarrow & 6x-5x& = &-27-42 \\\Leftrightarrow & x& = &-69 \\ & V = \left\{ -69 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (3x+4)& = & 14 \color{red}{-} (14+x) \\\Leftrightarrow & 18x+24& = &14-14-x \\\Leftrightarrow & 18x \color{red}{+24} & = &0 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 18x+x& = &0-24 \\\Leftrightarrow & 19x& = &-24 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-24}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-24}{19} & & \\ & V = \left\{ \frac{-24}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-2x+6)& = & -13 \color{red}{+} (-10-3x) \\\Leftrightarrow & -10x+30& = &-13-10-3x \\\Leftrightarrow & -10x \color{red}{+30} & = &-23 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{+30} \color{blue}{-30} \color{blue}{+3x} & = &-23 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-30} \\\Leftrightarrow & -10x+3x& = &-23-30 \\\Leftrightarrow & -7x& = &-53 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-53}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{53}{7} & & \\ & V = \left\{ \frac{53}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-6x-4)& = & -8 \color{red}{+} (-4+x) \\\Leftrightarrow & -12x-8& = &-8-4+x \\\Leftrightarrow & -12x \color{red}{-8} & = &-12 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &-12 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & -12x-x& = &-12+8 \\\Leftrightarrow & -13x& = &-4 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-4}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{4}{13} & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (4x-5)& = & 12 \color{red}{+} (2+x) \\\Leftrightarrow & 16x-20& = &12+2+x \\\Leftrightarrow & 16x \color{red}{-20} & = &14 \color{red}{+x} \\\Leftrightarrow & 16x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &14 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & 16x-x& = &14+20 \\\Leftrightarrow & 15x& = &34 \\\Leftrightarrow & \frac{15x}{ \color{red}{15} }& = &\frac{34}{ \color{red}{15} } \\\Leftrightarrow & x = \frac{34}{15} & & \\ & V = \left\{ \frac{34}{15} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-5x+2)& = & -3 \color{red}{+} (-6+x) \\\Leftrightarrow & -20x+8& = &-3-6+x \\\Leftrightarrow & -20x \color{red}{+8} & = &-9 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &-9 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & -20x-x& = &-9-8 \\\Leftrightarrow & -21x& = &-17 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-17}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{17}{21} & & \\ & V = \left\{ \frac{17}{21} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-4x+7)& = & 9 \color{red}{+} (2+x) \\\Leftrightarrow & -12x+21& = &9+2+x \\\Leftrightarrow & -12x \color{red}{+21} & = &11 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+21} \color{blue}{-21} \color{blue}{-x} & = &11 \color{red}{+x} \color{blue}{-x} \color{blue}{-21} \\\Leftrightarrow & -12x-x& = &11-21 \\\Leftrightarrow & -13x& = &-10 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-10}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{10}{13} & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)