Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (4x+1)& = & -13 \color{red}{-} (13+x) \\\Leftrightarrow & 12x+3& = &-13-13-x \\\Leftrightarrow & 12x \color{red}{+3} & = &-26 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+3} \color{blue}{-3} \color{blue}{+x} & = &-26 \color{red}{-x} \color{blue}{+x} \color{blue}{-3} \\\Leftrightarrow & 12x+x& = &-26-3 \\\Leftrightarrow & 13x& = &-29 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-29}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-29}{13} & & \\ & V = \left\{ \frac{-29}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-2x+3)& = & -8 \color{red}{-} (14+x) \\\Leftrightarrow & -4x+6& = &-8-14-x \\\Leftrightarrow & -4x \color{red}{+6} & = &-22 \color{red}{-x} \\\Leftrightarrow & -4x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &-22 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & -4x+x& = &-22-6 \\\Leftrightarrow & -3x& = &-28 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-28}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{28}{3} & & \\ & V = \left\{ \frac{28}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (3x+5)& = & 7 \color{red}{-} (5-2x) \\\Leftrightarrow & 9x+15& = &7-5+2x \\\Leftrightarrow & 9x \color{red}{+15} & = &2 \color{red}{+2x} \\\Leftrightarrow & 9x \color{red}{+15} \color{blue}{-15} \color{blue}{-2x} & = &2 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-15} \\\Leftrightarrow & 9x-2x& = &2-15 \\\Leftrightarrow & 7x& = &-13 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-13}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-13}{7} & & \\ & V = \left\{ \frac{-13}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-5x-3)& = & 5 \color{red}{-} (3+x) \\\Leftrightarrow & -25x-15& = &5-3-x \\\Leftrightarrow & -25x \color{red}{-15} & = &2 \color{red}{-x} \\\Leftrightarrow & -25x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & -25x+x& = &2+15 \\\Leftrightarrow & -24x& = &17 \\\Leftrightarrow & \frac{-24x}{ \color{red}{-24} }& = &\frac{17}{ \color{red}{-24} } \\\Leftrightarrow & x = \frac{-17}{24} & & \\ & V = \left\{ \frac{-17}{24} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-2x+3)& = & -3 \color{red}{-} (-14+x) \\\Leftrightarrow & -10x+15& = &-3+14-x \\\Leftrightarrow & -10x \color{red}{+15} & = &11 \color{red}{-x} \\\Leftrightarrow & -10x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & -10x+x& = &11-15 \\\Leftrightarrow & -9x& = &-4 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-4}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{4}{9} & & \\ & V = \left\{ \frac{4}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (x+3)& = & -8 \color{red}{+} (-13+3x) \\\Leftrightarrow & 2x+6& = &-8-13+3x \\\Leftrightarrow & 2x \color{red}{+6} & = &-21 \color{red}{+3x} \\\Leftrightarrow & 2x \color{red}{+6} \color{blue}{-6} \color{blue}{-3x} & = &-21 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-6} \\\Leftrightarrow & 2x-3x& = &-21-6 \\\Leftrightarrow & -x& = &-27 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-27}{ \color{red}{-1} } \\\Leftrightarrow & x = 27 & & \\ & V = \left\{ 27 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (6x-6)& = & 15 \color{red}{+} (11+x) \\\Leftrightarrow & 30x-30& = &15+11+x \\\Leftrightarrow & 30x \color{red}{-30} & = &26 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &26 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & 30x-x& = &26+30 \\\Leftrightarrow & 29x& = &56 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{56}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{56}{29} & & \\ & V = \left\{ \frac{56}{29} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-4x+7)& = & -7 \color{red}{-} (9+3x) \\\Leftrightarrow & -16x+28& = &-7-9-3x \\\Leftrightarrow & -16x \color{red}{+28} & = &-16 \color{red}{-3x} \\\Leftrightarrow & -16x \color{red}{+28} \color{blue}{-28} \color{blue}{+3x} & = &-16 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-28} \\\Leftrightarrow & -16x+3x& = &-16-28 \\\Leftrightarrow & -13x& = &-44 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-44}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{44}{13} & & \\ & V = \left\{ \frac{44}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (4x-1)& = & -13 \color{red}{-} (4+x) \\\Leftrightarrow & 12x-3& = &-13-4-x \\\Leftrightarrow & 12x \color{red}{-3} & = &-17 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-3} \color{blue}{+3} \color{blue}{+x} & = &-17 \color{red}{-x} \color{blue}{+x} \color{blue}{+3} \\\Leftrightarrow & 12x+x& = &-17+3 \\\Leftrightarrow & 13x& = &-14 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-14}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-14}{13} & & \\ & V = \left\{ \frac{-14}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-6x-5)& = & -5 \color{red}{+} (8+x) \\\Leftrightarrow & -36x-30& = &-5+8+x \\\Leftrightarrow & -36x \color{red}{-30} & = &3 \color{red}{+x} \\\Leftrightarrow & -36x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & -36x-x& = &3+30 \\\Leftrightarrow & -37x& = &33 \\\Leftrightarrow & \frac{-37x}{ \color{red}{-37} }& = &\frac{33}{ \color{red}{-37} } \\\Leftrightarrow & x = \frac{-33}{37} & & \\ & V = \left\{ \frac{-33}{37} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-4x-1)& = & 9 \color{red}{-} (-7+3x) \\\Leftrightarrow & -20x-5& = &9+7-3x \\\Leftrightarrow & -20x \color{red}{-5} & = &16 \color{red}{-3x} \\\Leftrightarrow & -20x \color{red}{-5} \color{blue}{+5} \color{blue}{+3x} & = &16 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+5} \\\Leftrightarrow & -20x+3x& = &16+5 \\\Leftrightarrow & -17x& = &21 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{21}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-21}{17} & & \\ & V = \left\{ \frac{-21}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (3x+4)& = & -9 \color{red}{+} (3+x) \\\Leftrightarrow & 9x+12& = &-9+3+x \\\Leftrightarrow & 9x \color{red}{+12} & = &-6 \color{red}{+x} \\\Leftrightarrow & 9x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 9x-x& = &-6-12 \\\Leftrightarrow & 8x& = &-18 \\\Leftrightarrow & \frac{8x}{ \color{red}{8} }& = &\frac{-18}{ \color{red}{8} } \\\Leftrightarrow & x = \frac{-9}{4} & & \\ & V = \left\{ \frac{-9}{4} \right\} & \\\end{align}\)