Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (4x+3)& = & 7 \color{red}{-} (-14+x) \\\Leftrightarrow & 8x+6& = &7+14-x \\\Leftrightarrow & 8x \color{red}{+6} & = &21 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &21 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 8x+x& = &21-6 \\\Leftrightarrow & 9x& = &15 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{15}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{5}{3} & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (x-3)& = & -8 \color{red}{+} (15+x) \\\Leftrightarrow & 3x-9& = &-8+15+x \\\Leftrightarrow & 3x \color{red}{-9} & = &7 \color{red}{+x} \\\Leftrightarrow & 3x \color{red}{-9} \color{blue}{+9} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{+9} \\\Leftrightarrow & 3x-x& = &7+9 \\\Leftrightarrow & 2x& = &16 \\\Leftrightarrow & \frac{2x}{ \color{red}{2} }& = &\frac{16}{ \color{red}{2} } \\\Leftrightarrow & x = 8 & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (4x-4)& = & 12 \color{red}{+} (2-5x) \\\Leftrightarrow & 16x-16& = &12+2-5x \\\Leftrightarrow & 16x \color{red}{-16} & = &14 \color{red}{-5x} \\\Leftrightarrow & 16x \color{red}{-16} \color{blue}{+16} \color{blue}{+5x} & = &14 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+16} \\\Leftrightarrow & 16x+5x& = &14+16 \\\Leftrightarrow & 21x& = &30 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{30}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{10}{7} & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-3x-5)& = & 11 \color{red}{+} (-15+x) \\\Leftrightarrow & -15x-25& = &11-15+x \\\Leftrightarrow & -15x \color{red}{-25} & = &-4 \color{red}{+x} \\\Leftrightarrow & -15x \color{red}{-25} \color{blue}{+25} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{+25} \\\Leftrightarrow & -15x-x& = &-4+25 \\\Leftrightarrow & -16x& = &21 \\\Leftrightarrow & \frac{-16x}{ \color{red}{-16} }& = &\frac{21}{ \color{red}{-16} } \\\Leftrightarrow & x = \frac{-21}{16} & & \\ & V = \left\{ \frac{-21}{16} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-2x-7)& = & 15 \color{red}{-} (-7+x) \\\Leftrightarrow & -4x-14& = &15+7-x \\\Leftrightarrow & -4x \color{red}{-14} & = &22 \color{red}{-x} \\\Leftrightarrow & -4x \color{red}{-14} \color{blue}{+14} \color{blue}{+x} & = &22 \color{red}{-x} \color{blue}{+x} \color{blue}{+14} \\\Leftrightarrow & -4x+x& = &22+14 \\\Leftrightarrow & -3x& = &36 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{36}{ \color{red}{-3} } \\\Leftrightarrow & x = -12 & & \\ & V = \left\{ -12 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (6x+5)& = & 12 \color{red}{-} (-5+x) \\\Leftrightarrow & 30x+25& = &12+5-x \\\Leftrightarrow & 30x \color{red}{+25} & = &17 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+25} \color{blue}{-25} \color{blue}{+x} & = &17 \color{red}{-x} \color{blue}{+x} \color{blue}{-25} \\\Leftrightarrow & 30x+x& = &17-25 \\\Leftrightarrow & 31x& = &-8 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-8}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-8}{31} & & \\ & V = \left\{ \frac{-8}{31} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (5x+5)& = & 8 \color{red}{-} (5+x) \\\Leftrightarrow & 10x+10& = &8-5-x \\\Leftrightarrow & 10x \color{red}{+10} & = &3 \color{red}{-x} \\\Leftrightarrow & 10x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & 10x+x& = &3-10 \\\Leftrightarrow & 11x& = &-7 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-7}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-7}{11} & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-6x+4)& = & 6 \color{red}{+} (-3+x) \\\Leftrightarrow & -30x+20& = &6-3+x \\\Leftrightarrow & -30x \color{red}{+20} & = &3 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & -30x-x& = &3-20 \\\Leftrightarrow & -31x& = &-17 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-17}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{17}{31} & & \\ & V = \left\{ \frac{17}{31} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-6x-5)& = & 8 \color{red}{-} (-15+x) \\\Leftrightarrow & -18x-15& = &8+15-x \\\Leftrightarrow & -18x \color{red}{-15} & = &23 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &23 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & -18x+x& = &23+15 \\\Leftrightarrow & -17x& = &38 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{38}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-38}{17} & & \\ & V = \left\{ \frac{-38}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (6x-2)& = & -8 \color{red}{-} (-11-5x) \\\Leftrightarrow & 36x-12& = &-8+11+5x \\\Leftrightarrow & 36x \color{red}{-12} & = &3 \color{red}{+5x} \\\Leftrightarrow & 36x \color{red}{-12} \color{blue}{+12} \color{blue}{-5x} & = &3 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+12} \\\Leftrightarrow & 36x-5x& = &3+12 \\\Leftrightarrow & 31x& = &15 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{15}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{15}{31} & & \\ & V = \left\{ \frac{15}{31} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (3x-7)& = & -7 \color{red}{-} (4+2x) \\\Leftrightarrow & 15x-35& = &-7-4-2x \\\Leftrightarrow & 15x \color{red}{-35} & = &-11 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{-35} \color{blue}{+35} \color{blue}{+2x} & = &-11 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+35} \\\Leftrightarrow & 15x+2x& = &-11+35 \\\Leftrightarrow & 17x& = &24 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{24}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{24}{17} & & \\ & V = \left\{ \frac{24}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-5x+2)& = & -9 \color{red}{-} (1+x) \\\Leftrightarrow & -10x+4& = &-9-1-x \\\Leftrightarrow & -10x \color{red}{+4} & = &-10 \color{red}{-x} \\\Leftrightarrow & -10x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & -10x+x& = &-10-4 \\\Leftrightarrow & -9x& = &-14 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-14}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{14}{9} & & \\ & V = \left\{ \frac{14}{9} \right\} & \\\end{align}\)