Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{5}{11})& = & -8x+\frac{6}{5} \\\Leftrightarrow & -21x+\frac{35}{11}& = & -8x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1155}{ \color{blue}{55} }x+ \frac{175}{ \color{blue}{55} })& = & (\frac{-440}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1155x \color{red}{+175} & = & \color{red}{-440x} +66 \\\Leftrightarrow & -1155x \color{red}{+175} \color{blue}{-175} \color{blue}{+440x} & = & \color{red}{-440x} +66 \color{blue}{+440x} \color{blue}{-175} \\\Leftrightarrow & -1155x+440x& = & 66-175 \\\Leftrightarrow & \color{red}{-715} x& = & -109 \\\Leftrightarrow & x = \frac{-109}{-715} & & \\\Leftrightarrow & x = \frac{109}{715} & & \\ & V = \left\{ \frac{109}{715} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{3}{7})& = & -5x+\frac{4}{11} \\\Leftrightarrow & -4x+\frac{6}{7}& = & -5x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-308}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -308x \color{red}{+66} & = & \color{red}{-385x} +28 \\\Leftrightarrow & -308x \color{red}{+66} \color{blue}{-66} \color{blue}{+385x} & = & \color{red}{-385x} +28 \color{blue}{+385x} \color{blue}{-66} \\\Leftrightarrow & -308x+385x& = & 28-66 \\\Leftrightarrow & \color{red}{77} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{77} & & \\ & V = \left\{ \frac{-38}{77} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{2}{7})& = & -5x+\frac{2}{11} \\\Leftrightarrow & -12x+\frac{6}{7}& = & -5x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{+66} & = & \color{red}{-385x} +14 \\\Leftrightarrow & -924x \color{red}{+66} \color{blue}{-66} \color{blue}{+385x} & = & \color{red}{-385x} +14 \color{blue}{+385x} \color{blue}{-66} \\\Leftrightarrow & -924x+385x& = & 14-66 \\\Leftrightarrow & \color{red}{-539} x& = & -52 \\\Leftrightarrow & x = \frac{-52}{-539} & & \\\Leftrightarrow & x = \frac{52}{539} & & \\ & V = \left\{ \frac{52}{539} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{5}{7})& = & 7x+\frac{7}{8} \\\Leftrightarrow & 30x-\frac{30}{7}& = & 7x+\frac{7}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1680}{ \color{blue}{56} }x- \frac{240}{ \color{blue}{56} })& = & (\frac{392}{ \color{blue}{56} }x+ \frac{49}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1680x \color{red}{-240} & = & \color{red}{392x} +49 \\\Leftrightarrow & 1680x \color{red}{-240} \color{blue}{+240} \color{blue}{-392x} & = & \color{red}{392x} +49 \color{blue}{-392x} \color{blue}{+240} \\\Leftrightarrow & 1680x-392x& = & 49+240 \\\Leftrightarrow & \color{red}{1288} x& = & 289 \\\Leftrightarrow & x = \frac{289}{1288} & & \\ & V = \left\{ \frac{289}{1288} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{2}{3})& = & -3x+\frac{9}{2} \\\Leftrightarrow & -8x-\frac{4}{3}& = & -3x+\frac{9}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-48}{ \color{blue}{6} }x- \frac{8}{ \color{blue}{6} })& = & (\frac{-18}{ \color{blue}{6} }x+ \frac{27}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -48x \color{red}{-8} & = & \color{red}{-18x} +27 \\\Leftrightarrow & -48x \color{red}{-8} \color{blue}{+8} \color{blue}{+18x} & = & \color{red}{-18x} +27 \color{blue}{+18x} \color{blue}{+8} \\\Leftrightarrow & -48x+18x& = & 27+8 \\\Leftrightarrow & \color{red}{-30} x& = & 35 \\\Leftrightarrow & x = \frac{35}{-30} & & \\\Leftrightarrow & x = \frac{-7}{6} & & \\ & V = \left\{ \frac{-7}{6} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{4}{3})& = & -8x+\frac{6}{11} \\\Leftrightarrow & 21x-\frac{28}{3}& = & -8x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{693}{ \color{blue}{33} }x- \frac{308}{ \color{blue}{33} })& = & (\frac{-264}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 693x \color{red}{-308} & = & \color{red}{-264x} +18 \\\Leftrightarrow & 693x \color{red}{-308} \color{blue}{+308} \color{blue}{+264x} & = & \color{red}{-264x} +18 \color{blue}{+264x} \color{blue}{+308} \\\Leftrightarrow & 693x+264x& = & 18+308 \\\Leftrightarrow & \color{red}{957} x& = & 326 \\\Leftrightarrow & x = \frac{326}{957} & & \\ & V = \left\{ \frac{326}{957} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{5}{7})& = & 5x+\frac{9}{10} \\\Leftrightarrow & -18x-\frac{30}{7}& = & 5x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-1260}{ \color{blue}{70} }x- \frac{300}{ \color{blue}{70} })& = & (\frac{350}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -1260x \color{red}{-300} & = & \color{red}{350x} +63 \\\Leftrightarrow & -1260x \color{red}{-300} \color{blue}{+300} \color{blue}{-350x} & = & \color{red}{350x} +63 \color{blue}{-350x} \color{blue}{+300} \\\Leftrightarrow & -1260x-350x& = & 63+300 \\\Leftrightarrow & \color{red}{-1610} x& = & 363 \\\Leftrightarrow & x = \frac{363}{-1610} & & \\\Leftrightarrow & x = \frac{-363}{1610} & & \\ & V = \left\{ \frac{-363}{1610} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{3}{8})& = & 3x+\frac{5}{6} \\\Leftrightarrow & 25x-\frac{15}{8}& = & 3x+\frac{5}{6} \\ & & & \text{kgv van noemers 8 en 6 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{600}{ \color{blue}{24} }x- \frac{45}{ \color{blue}{24} })& = & (\frac{72}{ \color{blue}{24} }x+ \frac{20}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 600x \color{red}{-45} & = & \color{red}{72x} +20 \\\Leftrightarrow & 600x \color{red}{-45} \color{blue}{+45} \color{blue}{-72x} & = & \color{red}{72x} +20 \color{blue}{-72x} \color{blue}{+45} \\\Leftrightarrow & 600x-72x& = & 20+45 \\\Leftrightarrow & \color{red}{528} x& = & 65 \\\Leftrightarrow & x = \frac{65}{528} & & \\ & V = \left\{ \frac{65}{528} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{3}{8})& = & 8x+\frac{2}{7} \\\Leftrightarrow & 21x+\frac{21}{8}& = & 8x+\frac{2}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1176}{ \color{blue}{56} }x+ \frac{147}{ \color{blue}{56} })& = & (\frac{448}{ \color{blue}{56} }x+ \frac{16}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1176x \color{red}{+147} & = & \color{red}{448x} +16 \\\Leftrightarrow & 1176x \color{red}{+147} \color{blue}{-147} \color{blue}{-448x} & = & \color{red}{448x} +16 \color{blue}{-448x} \color{blue}{-147} \\\Leftrightarrow & 1176x-448x& = & 16-147 \\\Leftrightarrow & \color{red}{728} x& = & -131 \\\Leftrightarrow & x = \frac{-131}{728} & & \\ & V = \left\{ \frac{-131}{728} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{5}{7})& = & -3x+\frac{8}{7} \\\Leftrightarrow & -8x+\frac{10}{7}& = & -3x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-56}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} })& = & (\frac{-21}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -56x \color{red}{+10} & = & \color{red}{-21x} +8 \\\Leftrightarrow & -56x \color{red}{+10} \color{blue}{-10} \color{blue}{+21x} & = & \color{red}{-21x} +8 \color{blue}{+21x} \color{blue}{-10} \\\Leftrightarrow & -56x+21x& = & 8-10 \\\Leftrightarrow & \color{red}{-35} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-35} & & \\\Leftrightarrow & x = \frac{2}{35} & & \\ & V = \left\{ \frac{2}{35} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{4}{11})& = & -7x+\frac{7}{2} \\\Leftrightarrow & 30x+\frac{24}{11}& = & -7x+\frac{7}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{660}{ \color{blue}{22} }x+ \frac{48}{ \color{blue}{22} })& = & (\frac{-154}{ \color{blue}{22} }x+ \frac{77}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 660x \color{red}{+48} & = & \color{red}{-154x} +77 \\\Leftrightarrow & 660x \color{red}{+48} \color{blue}{-48} \color{blue}{+154x} & = & \color{red}{-154x} +77 \color{blue}{+154x} \color{blue}{-48} \\\Leftrightarrow & 660x+154x& = & 77-48 \\\Leftrightarrow & \color{red}{814} x& = & 29 \\\Leftrightarrow & x = \frac{29}{814} & & \\ & V = \left\{ \frac{29}{814} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{5}{8})& = & -3x+\frac{6}{11} \\\Leftrightarrow & -14x+\frac{35}{8}& = & -3x+\frac{6}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1232}{ \color{blue}{88} }x+ \frac{385}{ \color{blue}{88} })& = & (\frac{-264}{ \color{blue}{88} }x+ \frac{48}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1232x \color{red}{+385} & = & \color{red}{-264x} +48 \\\Leftrightarrow & -1232x \color{red}{+385} \color{blue}{-385} \color{blue}{+264x} & = & \color{red}{-264x} +48 \color{blue}{+264x} \color{blue}{-385} \\\Leftrightarrow & -1232x+264x& = & 48-385 \\\Leftrightarrow & \color{red}{-968} x& = & -337 \\\Leftrightarrow & x = \frac{-337}{-968} & & \\\Leftrightarrow & x = \frac{337}{968} & & \\ & V = \left\{ \frac{337}{968} \right\} & \\\end{align}\)