Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{4}{7})& = & -3x+\frac{3}{10} \\\Leftrightarrow & 16x+\frac{16}{7}& = & -3x+\frac{3}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{1120}{ \color{blue}{70} }x+ \frac{160}{ \color{blue}{70} })& = & (\frac{-210}{ \color{blue}{70} }x+ \frac{21}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 1120x \color{red}{+160} & = & \color{red}{-210x} +21 \\\Leftrightarrow & 1120x \color{red}{+160} \color{blue}{-160} \color{blue}{+210x} & = & \color{red}{-210x} +21 \color{blue}{+210x} \color{blue}{-160} \\\Leftrightarrow & 1120x+210x& = & 21-160 \\\Leftrightarrow & \color{red}{1330} x& = & -139 \\\Leftrightarrow & x = \frac{-139}{1330} & & \\ & V = \left\{ \frac{-139}{1330} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{5}{7})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -10x+\frac{25}{7}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-210}{ \color{blue}{21} }x+ \frac{75}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -210x \color{red}{+75} & = & \color{red}{147x} +14 \\\Leftrightarrow & -210x \color{red}{+75} \color{blue}{-75} \color{blue}{-147x} & = & \color{red}{147x} +14 \color{blue}{-147x} \color{blue}{-75} \\\Leftrightarrow & -210x-147x& = & 14-75 \\\Leftrightarrow & \color{red}{-357} x& = & -61 \\\Leftrightarrow & x = \frac{-61}{-357} & & \\\Leftrightarrow & x = \frac{61}{357} & & \\ & V = \left\{ \frac{61}{357} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{4}{7})& = & -5x+\frac{9}{4} \\\Leftrightarrow & -9x-\frac{12}{7}& = & -5x+\frac{9}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-252}{ \color{blue}{28} }x- \frac{48}{ \color{blue}{28} })& = & (\frac{-140}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -252x \color{red}{-48} & = & \color{red}{-140x} +63 \\\Leftrightarrow & -252x \color{red}{-48} \color{blue}{+48} \color{blue}{+140x} & = & \color{red}{-140x} +63 \color{blue}{+140x} \color{blue}{+48} \\\Leftrightarrow & -252x+140x& = & 63+48 \\\Leftrightarrow & \color{red}{-112} x& = & 111 \\\Leftrightarrow & x = \frac{111}{-112} & & \\\Leftrightarrow & x = \frac{-111}{112} & & \\ & V = \left\{ \frac{-111}{112} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{5}{7})& = & -7x+\frac{7}{5} \\\Leftrightarrow & 16x+\frac{20}{7}& = & -7x+\frac{7}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{560}{ \color{blue}{35} }x+ \frac{100}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{49}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 560x \color{red}{+100} & = & \color{red}{-245x} +49 \\\Leftrightarrow & 560x \color{red}{+100} \color{blue}{-100} \color{blue}{+245x} & = & \color{red}{-245x} +49 \color{blue}{+245x} \color{blue}{-100} \\\Leftrightarrow & 560x+245x& = & 49-100 \\\Leftrightarrow & \color{red}{805} x& = & -51 \\\Leftrightarrow & x = \frac{-51}{805} & & \\ & V = \left\{ \frac{-51}{805} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{2}{9})& = & -7x+\frac{9}{2} \\\Leftrightarrow & 20x+\frac{8}{9}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{360}{ \color{blue}{18} }x+ \frac{16}{ \color{blue}{18} })& = & (\frac{-126}{ \color{blue}{18} }x+ \frac{81}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 360x \color{red}{+16} & = & \color{red}{-126x} +81 \\\Leftrightarrow & 360x \color{red}{+16} \color{blue}{-16} \color{blue}{+126x} & = & \color{red}{-126x} +81 \color{blue}{+126x} \color{blue}{-16} \\\Leftrightarrow & 360x+126x& = & 81-16 \\\Leftrightarrow & \color{red}{486} x& = & 65 \\\Leftrightarrow & x = \frac{65}{486} & & \\ & V = \left\{ \frac{65}{486} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{5}{8})& = & -7x+\frac{2}{3} \\\Leftrightarrow & -6x+\frac{15}{8}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-144}{ \color{blue}{24} }x+ \frac{45}{ \color{blue}{24} })& = & (\frac{-168}{ \color{blue}{24} }x+ \frac{16}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -144x \color{red}{+45} & = & \color{red}{-168x} +16 \\\Leftrightarrow & -144x \color{red}{+45} \color{blue}{-45} \color{blue}{+168x} & = & \color{red}{-168x} +16 \color{blue}{+168x} \color{blue}{-45} \\\Leftrightarrow & -144x+168x& = & 16-45 \\\Leftrightarrow & \color{red}{24} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{24} & & \\ & V = \left\{ \frac{-29}{24} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{2}{11})& = & -2x+\frac{9}{7} \\\Leftrightarrow & 25x-\frac{10}{11}& = & -2x+\frac{9}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1925}{ \color{blue}{77} }x- \frac{70}{ \color{blue}{77} })& = & (\frac{-154}{ \color{blue}{77} }x+ \frac{99}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1925x \color{red}{-70} & = & \color{red}{-154x} +99 \\\Leftrightarrow & 1925x \color{red}{-70} \color{blue}{+70} \color{blue}{+154x} & = & \color{red}{-154x} +99 \color{blue}{+154x} \color{blue}{+70} \\\Leftrightarrow & 1925x+154x& = & 99+70 \\\Leftrightarrow & \color{red}{2079} x& = & 169 \\\Leftrightarrow & x = \frac{169}{2079} & & \\ & V = \left\{ \frac{169}{2079} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{5}{9})& = & -5x+\frac{6}{7} \\\Leftrightarrow & -28x-\frac{35}{9}& = & -5x+\frac{6}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1764}{ \color{blue}{63} }x- \frac{245}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1764x \color{red}{-245} & = & \color{red}{-315x} +54 \\\Leftrightarrow & -1764x \color{red}{-245} \color{blue}{+245} \color{blue}{+315x} & = & \color{red}{-315x} +54 \color{blue}{+315x} \color{blue}{+245} \\\Leftrightarrow & -1764x+315x& = & 54+245 \\\Leftrightarrow & \color{red}{-1449} x& = & 299 \\\Leftrightarrow & x = \frac{299}{-1449} & & \\\Leftrightarrow & x = \frac{-13}{63} & & \\ & V = \left\{ \frac{-13}{63} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{2}{5})& = & -7x+\frac{2}{7} \\\Leftrightarrow & 18x-\frac{12}{5}& = & -7x+\frac{2}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{630}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{10}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 630x \color{red}{-84} & = & \color{red}{-245x} +10 \\\Leftrightarrow & 630x \color{red}{-84} \color{blue}{+84} \color{blue}{+245x} & = & \color{red}{-245x} +10 \color{blue}{+245x} \color{blue}{+84} \\\Leftrightarrow & 630x+245x& = & 10+84 \\\Leftrightarrow & \color{red}{875} x& = & 94 \\\Leftrightarrow & x = \frac{94}{875} & & \\ & V = \left\{ \frac{94}{875} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{4}{7})& = & 3x+\frac{2}{7} \\\Leftrightarrow & 20x-\frac{16}{7}& = & 3x+\frac{2}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{140}{ \color{blue}{7} }x- \frac{16}{ \color{blue}{7} })& = & (\frac{21}{ \color{blue}{7} }x+ \frac{2}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 140x \color{red}{-16} & = & \color{red}{21x} +2 \\\Leftrightarrow & 140x \color{red}{-16} \color{blue}{+16} \color{blue}{-21x} & = & \color{red}{21x} +2 \color{blue}{-21x} \color{blue}{+16} \\\Leftrightarrow & 140x-21x& = & 2+16 \\\Leftrightarrow & \color{red}{119} x& = & 18 \\\Leftrightarrow & x = \frac{18}{119} & & \\ & V = \left\{ \frac{18}{119} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{3}{5})& = & 5x+\frac{2}{9} \\\Leftrightarrow & -12x+\frac{9}{5}& = & 5x+\frac{2}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-540}{ \color{blue}{45} }x+ \frac{81}{ \color{blue}{45} })& = & (\frac{225}{ \color{blue}{45} }x+ \frac{10}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -540x \color{red}{+81} & = & \color{red}{225x} +10 \\\Leftrightarrow & -540x \color{red}{+81} \color{blue}{-81} \color{blue}{-225x} & = & \color{red}{225x} +10 \color{blue}{-225x} \color{blue}{-81} \\\Leftrightarrow & -540x-225x& = & 10-81 \\\Leftrightarrow & \color{red}{-765} x& = & -71 \\\Leftrightarrow & x = \frac{-71}{-765} & & \\\Leftrightarrow & x = \frac{71}{765} & & \\ & V = \left\{ \frac{71}{765} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{2}{5})& = & 7x+\frac{6}{11} \\\Leftrightarrow & -30x+\frac{12}{5}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1650}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1650x \color{red}{+132} & = & \color{red}{385x} +30 \\\Leftrightarrow & -1650x \color{red}{+132} \color{blue}{-132} \color{blue}{-385x} & = & \color{red}{385x} +30 \color{blue}{-385x} \color{blue}{-132} \\\Leftrightarrow & -1650x-385x& = & 30-132 \\\Leftrightarrow & \color{red}{-2035} x& = & -102 \\\Leftrightarrow & x = \frac{-102}{-2035} & & \\\Leftrightarrow & x = \frac{102}{2035} & & \\ & V = \left\{ \frac{102}{2035} \right\} & \\\end{align}\)