Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-5x-4)& = & -7 \color{red}{+} (10-3x) \\\Leftrightarrow & -10x-8& = &-7+10-3x \\\Leftrightarrow & -10x \color{red}{-8} & = &3 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{-8} \color{blue}{+8} \color{blue}{+3x} & = &3 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+8} \\\Leftrightarrow & -10x+3x& = &3+8 \\\Leftrightarrow & -7x& = &11 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{11}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-11}{7} & & \\ & V = \left\{ \frac{-11}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-5x-1)& = & 6 \color{red}{-} (-10+3x) \\\Leftrightarrow & -25x-5& = &6+10-3x \\\Leftrightarrow & -25x \color{red}{-5} & = &16 \color{red}{-3x} \\\Leftrightarrow & -25x \color{red}{-5} \color{blue}{+5} \color{blue}{+3x} & = &16 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+5} \\\Leftrightarrow & -25x+3x& = &16+5 \\\Leftrightarrow & -22x& = &21 \\\Leftrightarrow & \frac{-22x}{ \color{red}{-22} }& = &\frac{21}{ \color{red}{-22} } \\\Leftrightarrow & x = \frac{-21}{22} & & \\ & V = \left\{ \frac{-21}{22} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-6x-4)& = & -1 \color{red}{-} (-12+x) \\\Leftrightarrow & -30x-20& = &-1+12-x \\\Leftrightarrow & -30x \color{red}{-20} & = &11 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & -30x+x& = &11+20 \\\Leftrightarrow & -29x& = &31 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{31}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-31}{29} & & \\ & V = \left\{ \frac{-31}{29} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-2x-5)& = & 12 \color{red}{-} (9+x) \\\Leftrightarrow & -8x-20& = &12-9-x \\\Leftrightarrow & -8x \color{red}{-20} & = &3 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & -8x+x& = &3+20 \\\Leftrightarrow & -7x& = &23 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{23}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-23}{7} & & \\ & V = \left\{ \frac{-23}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (6x-5)& = & -3 \color{red}{+} (9-5x) \\\Leftrightarrow & 18x-15& = &-3+9-5x \\\Leftrightarrow & 18x \color{red}{-15} & = &6 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{-15} \color{blue}{+15} \color{blue}{+5x} & = &6 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+15} \\\Leftrightarrow & 18x+5x& = &6+15 \\\Leftrightarrow & 23x& = &21 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{21}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{21}{23} & & \\ & V = \left\{ \frac{21}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-2x+4)& = & 6 \color{red}{-} (1+x) \\\Leftrightarrow & -8x+16& = &6-1-x \\\Leftrightarrow & -8x \color{red}{+16} & = &5 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{+16} \color{blue}{-16} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{-16} \\\Leftrightarrow & -8x+x& = &5-16 \\\Leftrightarrow & -7x& = &-11 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-11}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{11}{7} & & \\ & V = \left\{ \frac{11}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (5x+5)& = & 4 \color{red}{-} (8+x) \\\Leftrightarrow & 20x+20& = &4-8-x \\\Leftrightarrow & 20x \color{red}{+20} & = &-4 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & 20x+x& = &-4-20 \\\Leftrightarrow & 21x& = &-24 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-24}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-8}{7} & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-x-4)& = & 11 \color{red}{+} (11+3x) \\\Leftrightarrow & -5x-20& = &11+11+3x \\\Leftrightarrow & -5x \color{red}{-20} & = &22 \color{red}{+3x} \\\Leftrightarrow & -5x \color{red}{-20} \color{blue}{+20} \color{blue}{-3x} & = &22 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+20} \\\Leftrightarrow & -5x-3x& = &22+20 \\\Leftrightarrow & -8x& = &42 \\\Leftrightarrow & \frac{-8x}{ \color{red}{-8} }& = &\frac{42}{ \color{red}{-8} } \\\Leftrightarrow & x = \frac{-21}{4} & & \\ & V = \left\{ \frac{-21}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (x+6)& = & -4 \color{red}{+} (12-4x) \\\Leftrightarrow & 5x+30& = &-4+12-4x \\\Leftrightarrow & 5x \color{red}{+30} & = &8 \color{red}{-4x} \\\Leftrightarrow & 5x \color{red}{+30} \color{blue}{-30} \color{blue}{+4x} & = &8 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-30} \\\Leftrightarrow & 5x+4x& = &8-30 \\\Leftrightarrow & 9x& = &-22 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-22}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-22}{9} & & \\ & V = \left\{ \frac{-22}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-4x+7)& = & 12 \color{red}{-} (-9+x) \\\Leftrightarrow & -16x+28& = &12+9-x \\\Leftrightarrow & -16x \color{red}{+28} & = &21 \color{red}{-x} \\\Leftrightarrow & -16x \color{red}{+28} \color{blue}{-28} \color{blue}{+x} & = &21 \color{red}{-x} \color{blue}{+x} \color{blue}{-28} \\\Leftrightarrow & -16x+x& = &21-28 \\\Leftrightarrow & -15x& = &-7 \\\Leftrightarrow & \frac{-15x}{ \color{red}{-15} }& = &\frac{-7}{ \color{red}{-15} } \\\Leftrightarrow & x = \frac{7}{15} & & \\ & V = \left\{ \frac{7}{15} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (3x-2)& = & 6 \color{red}{-} (12-5x) \\\Leftrightarrow & 18x-12& = &6-12+5x \\\Leftrightarrow & 18x \color{red}{-12} & = &-6 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{-12} \color{blue}{+12} \color{blue}{-5x} & = &-6 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+12} \\\Leftrightarrow & 18x-5x& = &-6+12 \\\Leftrightarrow & 13x& = &6 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{6}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{6}{13} & & \\ & V = \left\{ \frac{6}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (2x-5)& = & 14 \color{red}{-} (-11+x) \\\Leftrightarrow & 6x-15& = &14+11-x \\\Leftrightarrow & 6x \color{red}{-15} & = &25 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &25 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & 6x+x& = &25+15 \\\Leftrightarrow & 7x& = &40 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{40}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{40}{7} & & \\ & V = \left\{ \frac{40}{7} \right\} & \\\end{align}\)