Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{5}{4})& = & -4x+\frac{5}{8} \\\Leftrightarrow & 9x+\frac{15}{4}& = & -4x+\frac{5}{8} \\ & & & \text{kgv van noemers 4 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{72}{ \color{blue}{8} }x+ \frac{30}{ \color{blue}{8} })& = & (\frac{-32}{ \color{blue}{8} }x+ \frac{5}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 72x \color{red}{+30} & = & \color{red}{-32x} +5 \\\Leftrightarrow & 72x \color{red}{+30} \color{blue}{-30} \color{blue}{+32x} & = & \color{red}{-32x} +5 \color{blue}{+32x} \color{blue}{-30} \\\Leftrightarrow & 72x+32x& = & 5-30 \\\Leftrightarrow & \color{red}{104} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{104} & & \\ & V = \left\{ \frac{-25}{104} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{2}{7})& = & 5x+\frac{9}{11} \\\Leftrightarrow & -12x-\frac{6}{7}& = & 5x+\frac{9}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x- \frac{66}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{63}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{-66} & = & \color{red}{385x} +63 \\\Leftrightarrow & -924x \color{red}{-66} \color{blue}{+66} \color{blue}{-385x} & = & \color{red}{385x} +63 \color{blue}{-385x} \color{blue}{+66} \\\Leftrightarrow & -924x-385x& = & 63+66 \\\Leftrightarrow & \color{red}{-1309} x& = & 129 \\\Leftrightarrow & x = \frac{129}{-1309} & & \\\Leftrightarrow & x = \frac{-129}{1309} & & \\ & V = \left\{ \frac{-129}{1309} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{2}{3})& = & -2x+\frac{7}{11} \\\Leftrightarrow & 35x-\frac{14}{3}& = & -2x+\frac{7}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{1155}{ \color{blue}{33} }x- \frac{154}{ \color{blue}{33} })& = & (\frac{-66}{ \color{blue}{33} }x+ \frac{21}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 1155x \color{red}{-154} & = & \color{red}{-66x} +21 \\\Leftrightarrow & 1155x \color{red}{-154} \color{blue}{+154} \color{blue}{+66x} & = & \color{red}{-66x} +21 \color{blue}{+66x} \color{blue}{+154} \\\Leftrightarrow & 1155x+66x& = & 21+154 \\\Leftrightarrow & \color{red}{1221} x& = & 175 \\\Leftrightarrow & x = \frac{175}{1221} & & \\ & V = \left\{ \frac{175}{1221} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{5}{4})& = & 2x+\frac{8}{7} \\\Leftrightarrow & 15x+\frac{15}{4}& = & 2x+\frac{8}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{420}{ \color{blue}{28} }x+ \frac{105}{ \color{blue}{28} })& = & (\frac{56}{ \color{blue}{28} }x+ \frac{32}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 420x \color{red}{+105} & = & \color{red}{56x} +32 \\\Leftrightarrow & 420x \color{red}{+105} \color{blue}{-105} \color{blue}{-56x} & = & \color{red}{56x} +32 \color{blue}{-56x} \color{blue}{-105} \\\Leftrightarrow & 420x-56x& = & 32-105 \\\Leftrightarrow & \color{red}{364} x& = & -73 \\\Leftrightarrow & x = \frac{-73}{364} & & \\ & V = \left\{ \frac{-73}{364} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{5}{9})& = & 5x+\frac{5}{8} \\\Leftrightarrow & 12x-\frac{20}{9}& = & 5x+\frac{5}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{864}{ \color{blue}{72} }x- \frac{160}{ \color{blue}{72} })& = & (\frac{360}{ \color{blue}{72} }x+ \frac{45}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 864x \color{red}{-160} & = & \color{red}{360x} +45 \\\Leftrightarrow & 864x \color{red}{-160} \color{blue}{+160} \color{blue}{-360x} & = & \color{red}{360x} +45 \color{blue}{-360x} \color{blue}{+160} \\\Leftrightarrow & 864x-360x& = & 45+160 \\\Leftrightarrow & \color{red}{504} x& = & 205 \\\Leftrightarrow & x = \frac{205}{504} & & \\ & V = \left\{ \frac{205}{504} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{4}{5})& = & -5x+\frac{7}{8} \\\Leftrightarrow & 6x+\frac{12}{5}& = & -5x+\frac{7}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{240}{ \color{blue}{40} }x+ \frac{96}{ \color{blue}{40} })& = & (\frac{-200}{ \color{blue}{40} }x+ \frac{35}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 240x \color{red}{+96} & = & \color{red}{-200x} +35 \\\Leftrightarrow & 240x \color{red}{+96} \color{blue}{-96} \color{blue}{+200x} & = & \color{red}{-200x} +35 \color{blue}{+200x} \color{blue}{-96} \\\Leftrightarrow & 240x+200x& = & 35-96 \\\Leftrightarrow & \color{red}{440} x& = & -61 \\\Leftrightarrow & x = \frac{-61}{440} & & \\ & V = \left\{ \frac{-61}{440} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{3}{7})& = & 5x+\frac{3}{5} \\\Leftrightarrow & 6x+\frac{6}{7}& = & 5x+\frac{3}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{210}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{21}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 210x \color{red}{+30} & = & \color{red}{175x} +21 \\\Leftrightarrow & 210x \color{red}{+30} \color{blue}{-30} \color{blue}{-175x} & = & \color{red}{175x} +21 \color{blue}{-175x} \color{blue}{-30} \\\Leftrightarrow & 210x-175x& = & 21-30 \\\Leftrightarrow & \color{red}{35} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{35} & & \\ & V = \left\{ \frac{-9}{35} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{2}{5})& = & 5x+\frac{8}{7} \\\Leftrightarrow & -12x-\frac{12}{5}& = & 5x+\frac{8}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{-84} & = & \color{red}{175x} +40 \\\Leftrightarrow & -420x \color{red}{-84} \color{blue}{+84} \color{blue}{-175x} & = & \color{red}{175x} +40 \color{blue}{-175x} \color{blue}{+84} \\\Leftrightarrow & -420x-175x& = & 40+84 \\\Leftrightarrow & \color{red}{-595} x& = & 124 \\\Leftrightarrow & x = \frac{124}{-595} & & \\\Leftrightarrow & x = \frac{-124}{595} & & \\ & V = \left\{ \frac{-124}{595} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{4}{5})& = & -8x+\frac{2}{11} \\\Leftrightarrow & -15x-\frac{12}{5}& = & -8x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-825}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{-440}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -825x \color{red}{-132} & = & \color{red}{-440x} +10 \\\Leftrightarrow & -825x \color{red}{-132} \color{blue}{+132} \color{blue}{+440x} & = & \color{red}{-440x} +10 \color{blue}{+440x} \color{blue}{+132} \\\Leftrightarrow & -825x+440x& = & 10+132 \\\Leftrightarrow & \color{red}{-385} x& = & 142 \\\Leftrightarrow & x = \frac{142}{-385} & & \\\Leftrightarrow & x = \frac{-142}{385} & & \\ & V = \left\{ \frac{-142}{385} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{5}{7})& = & -7x+\frac{9}{7} \\\Leftrightarrow & -30x+\frac{30}{7}& = & -7x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-210}{ \color{blue}{7} }x+ \frac{30}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -210x \color{red}{+30} & = & \color{red}{-49x} +9 \\\Leftrightarrow & -210x \color{red}{+30} \color{blue}{-30} \color{blue}{+49x} & = & \color{red}{-49x} +9 \color{blue}{+49x} \color{blue}{-30} \\\Leftrightarrow & -210x+49x& = & 9-30 \\\Leftrightarrow & \color{red}{-161} x& = & -21 \\\Leftrightarrow & x = \frac{-21}{-161} & & \\\Leftrightarrow & x = \frac{3}{23} & & \\ & V = \left\{ \frac{3}{23} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{3}{8})& = & 7x+\frac{10}{3} \\\Leftrightarrow & -10x-\frac{15}{8}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-240}{ \color{blue}{24} }x- \frac{45}{ \color{blue}{24} })& = & (\frac{168}{ \color{blue}{24} }x+ \frac{80}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -240x \color{red}{-45} & = & \color{red}{168x} +80 \\\Leftrightarrow & -240x \color{red}{-45} \color{blue}{+45} \color{blue}{-168x} & = & \color{red}{168x} +80 \color{blue}{-168x} \color{blue}{+45} \\\Leftrightarrow & -240x-168x& = & 80+45 \\\Leftrightarrow & \color{red}{-408} x& = & 125 \\\Leftrightarrow & x = \frac{125}{-408} & & \\\Leftrightarrow & x = \frac{-125}{408} & & \\ & V = \left\{ \frac{-125}{408} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{5}{7})& = & -7x+\frac{10}{3} \\\Leftrightarrow & -30x+\frac{30}{7}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-630}{ \color{blue}{21} }x+ \frac{90}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -630x \color{red}{+90} & = & \color{red}{-147x} +70 \\\Leftrightarrow & -630x \color{red}{+90} \color{blue}{-90} \color{blue}{+147x} & = & \color{red}{-147x} +70 \color{blue}{+147x} \color{blue}{-90} \\\Leftrightarrow & -630x+147x& = & 70-90 \\\Leftrightarrow & \color{red}{-483} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{-483} & & \\\Leftrightarrow & x = \frac{20}{483} & & \\ & V = \left\{ \frac{20}{483} \right\} & \\\end{align}\)